1 Chapter 2 Lab: Introduction to R

This one is indeed a soft intro!

No worry to make things wrong: TRY!

Got R?

Start…

  • an R script (tired!)
  • an R Markdown document (wired!)

1.1 Basic commands

Functions are noted as funcname(input1, input2) - inputs are called arguments

Creating a vector by concatenating

c(1, 3, 2, 5)
## [1] 1 3 2 5
x <- c(1, 3, 2, 5) # use <- for assignment, leave = for parameter values
x
## [1] 1 3 2 5
x = c(1,6,2)
y = c(1,4,3)

Navigating history:

  • up arrow
  • ctrl + up (RStudio) while typing part of the command

Help:

  • use ?
  • help(funcname)

Length (of a vector)

length(x)
## [1] 3
length(y)
## [1] 3

Adding things together

1 + 4
## [1] 5
x + y # if same length
## [1]  2 10  5
x + 1
## [1] 2 7 3
x + c(1,2)
## Warning in x + c(1, 2): longer object length is not a multiple of shorter object
## length
## [1] 2 8 3

Listing objects, removing them

ls()
## [1] "x" "y"
rm(x, y)
ls()
## character(0)

Create a matrix of numbers

?matrix
x <- matrix(data=c(1,2,3,4), nrow=2, ncol=2)
x
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4
x <- matrix(data=c(1,2,3,4), 2, 2)
x
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4
# Recommended: specify arguments!
matrix(c(1,2,3,4),2,2,byrow=TRUE)
##      [,1] [,2]
## [1,]    1    2
## [2,]    3    4

Squaring, squared root

x
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4
sqrt(x)
##          [,1]     [,2]
## [1,] 1.000000 1.732051
## [2,] 1.414214 2.000000
sqrt(x)[,1]
## [1] 1.000000 1.414214
x^2
##      [,1] [,2]
## [1,]    1    9
## [2,]    4   16

Random normal variables, with rnorm

# bonus - when dealing with random quantities!
set.seed(42)

x <- rnorm(50)
# default: mean of 0 and standard deviation of 1
y <- x + rnorm(50,mean=50,sd=.1) 

Computing the correlation between two sets of numbers

cor(x,y)
## [1] 0.9968525

Mean & Standard deviation

mean(x)
## [1] -0.03567178
sd(x)
## [1] 1.151476
mean(y)
## [1] 49.9744
sd(y)
## [1] 1.132932
var(x)
## [1] 1.325898
var(y)
## [1] 1.283535
set.seed(3)
y <- rnorm(100)
mean(y)
## [1] 0.01103557
var(y)
## [1] 0.7328675
sqrt(var(y))
## [1] 0.8560768
sd(y)
## [1] 0.8560768

1.2 Graphics

Meet the plot() function!

plot(x,y)

?plot

The plot() function is the primary way to plot data in R. For instance, plot(x,y) produces a scatterplot of the numbers in x versus the numbers in y. There are many additional options that can be passed in to the plot() function. For example, passing in the argument xlab will result in a label on the x-axis. To find out more information about the plot() function, type ?plot.

set.seed(42)
x <- rnorm(100)
y <- rnorm(100)
plot(x,y)

plot(x,y,
     xlab="this is the x-axis",
     ylab="this is the y-axis",
     main="Plot of X vs Y")

# plot()

Saving the output:

open device
plot...
close device
pdf("Figure.pdf")
plot(x,y,col="green")
dev.off()
## quartz_off_screen 
##                 2

Devices: pdf(), jpeg(), …

Creating sequences of numbers

?seq
seq(0,1)
## [1] 0 1
seq(0,1,length=10)
##  [1] 0.0000000 0.1111111 0.2222222 0.3333333 0.4444444 0.5555556 0.6666667
##  [8] 0.7777778 0.8888889 1.0000000
pi
## [1] 3.141593
seq(-pi,pi,length=50)
##  [1] -3.14159265 -3.01336438 -2.88513611 -2.75690784 -2.62867957 -2.50045130
##  [7] -2.37222302 -2.24399475 -2.11576648 -1.98753821 -1.85930994 -1.73108167
## [13] -1.60285339 -1.47462512 -1.34639685 -1.21816858 -1.08994031 -0.96171204
## [19] -0.83348377 -0.70525549 -0.57702722 -0.44879895 -0.32057068 -0.19234241
## [25] -0.06411414  0.06411414  0.19234241  0.32057068  0.44879895  0.57702722
## [31]  0.70525549  0.83348377  0.96171204  1.08994031  1.21816858  1.34639685
## [37]  1.47462512  1.60285339  1.73108167  1.85930994  1.98753821  2.11576648
## [43]  2.24399475  2.37222302  2.50045130  2.62867957  2.75690784  2.88513611
## [49]  3.01336438  3.14159265

Some more complex plots:

  • contour() to represent 3d data
?contour
?outer

# assignment and printing trick ;)
(x <- seq(-pi,pi,length=50))
##  [1] -3.14159265 -3.01336438 -2.88513611 -2.75690784 -2.62867957 -2.50045130
##  [7] -2.37222302 -2.24399475 -2.11576648 -1.98753821 -1.85930994 -1.73108167
## [13] -1.60285339 -1.47462512 -1.34639685 -1.21816858 -1.08994031 -0.96171204
## [19] -0.83348377 -0.70525549 -0.57702722 -0.44879895 -0.32057068 -0.19234241
## [25] -0.06411414  0.06411414  0.19234241  0.32057068  0.44879895  0.57702722
## [31]  0.70525549  0.83348377  0.96171204  1.08994031  1.21816858  1.34639685
## [37]  1.47462512  1.60285339  1.73108167  1.85930994  1.98753821  2.11576648
## [43]  2.24399475  2.37222302  2.50045130  2.62867957  2.75690784  2.88513611
## [49]  3.01336438  3.14159265
y <- x
f <- outer(x,y,function (x,y)cos(y)/(1+x^2))
f
##              [,1]        [,2]        [,3]        [,4]        [,5]        [,6]
##  [1,] -0.09199967 -0.09124435 -0.08899081 -0.08527603 -0.08016103 -0.07372979
##  [2,] -0.09920276 -0.09838830 -0.09595832 -0.09195270 -0.08643722 -0.07950244
##  [3,] -0.10724999 -0.10636947 -0.10374236 -0.09941181 -0.09344892 -0.08595160
##  [4,] -0.11627176 -0.11531717 -0.11246907 -0.10777424 -0.10130976 -0.09318177
##  [5,] -0.12642295 -0.12538502 -0.12228827 -0.11718355 -0.11015468 -0.10131707
##  [6,] -0.13788811 -0.13675606 -0.13337846 -0.12781080 -0.12014449 -0.11050541
##  [7,] -0.15088778 -0.14964899 -0.14595297 -0.13986041 -0.13147134 -0.12092352
##  [8,] -0.16568601 -0.16432573 -0.16026723 -0.15357714 -0.14436532 -0.13278303
##  [9,] -0.18259945 -0.18110031 -0.17662751 -0.16925449 -0.15910231 -0.14633769
## [10,] -0.20200763 -0.20034915 -0.19540094 -0.18724425 -0.17601302 -0.16189166
## [11,] -0.22436448 -0.22252245 -0.21702661 -0.20796720 -0.19549297 -0.17980875
## [12,] -0.25020994 -0.24815572 -0.24202679 -0.23192379 -0.21801260 -0.20052166
## [13,] -0.28017962 -0.27787935 -0.27101630 -0.25970318 -0.24412574 -0.22453976
## [14,] -0.31500833 -0.31242211 -0.30470594 -0.29198650 -0.27447265 -0.25245196
## [15,] -0.35551960 -0.35260078 -0.34389228 -0.32953707 -0.30977087 -0.28491825
## [16,] -0.40258707 -0.39928184 -0.38942041 -0.37316471 -0.35078165 -0.32263877
## [17,] -0.45704468 -0.45329235 -0.44209697 -0.42364238 -0.39823158 -0.36628184
## [18,] -0.51951019 -0.51524502 -0.50251954 -0.48154270 -0.45265895 -0.41634255
## [19,] -0.59007662 -0.58523209 -0.57077808 -0.54695190 -0.51414479 -0.47289544
## [20,] -0.66783078 -0.66234790 -0.64598928 -0.61902354 -0.58189345 -0.53520868
## [21,] -0.75020983 -0.74405061 -0.72567411 -0.69538206 -0.65367185 -0.60122837
## [22,] -0.83234804 -0.82551448 -0.80512599 -0.77151735 -0.72524042 -0.66705506
## [23,] -0.90681105 -0.89936615 -0.87715367 -0.84053836 -0.79012143 -0.72673073
## [24,] -0.96432424 -0.95640716 -0.93278589 -0.89384830 -0.84023375 -0.77282259
## [25,] -0.99590621 -0.98772983 -0.96333496 -0.92312215 -0.86775170 -0.79813280
## [26,] -0.99590621 -0.98772983 -0.96333496 -0.92312215 -0.86775170 -0.79813280
## [27,] -0.96432424 -0.95640716 -0.93278589 -0.89384830 -0.84023375 -0.77282259
## [28,] -0.90681105 -0.89936615 -0.87715367 -0.84053836 -0.79012143 -0.72673073
## [29,] -0.83234804 -0.82551448 -0.80512599 -0.77151735 -0.72524042 -0.66705506
## [30,] -0.75020983 -0.74405061 -0.72567411 -0.69538206 -0.65367185 -0.60122837
## [31,] -0.66783078 -0.66234790 -0.64598928 -0.61902354 -0.58189345 -0.53520868
## [32,] -0.59007662 -0.58523209 -0.57077808 -0.54695190 -0.51414479 -0.47289544
## [33,] -0.51951019 -0.51524502 -0.50251954 -0.48154270 -0.45265895 -0.41634255
## [34,] -0.45704468 -0.45329235 -0.44209697 -0.42364238 -0.39823158 -0.36628184
## [35,] -0.40258707 -0.39928184 -0.38942041 -0.37316471 -0.35078165 -0.32263877
## [36,] -0.35551960 -0.35260078 -0.34389228 -0.32953707 -0.30977087 -0.28491825
## [37,] -0.31500833 -0.31242211 -0.30470594 -0.29198650 -0.27447265 -0.25245196
## [38,] -0.28017962 -0.27787935 -0.27101630 -0.25970318 -0.24412574 -0.22453976
## [39,] -0.25020994 -0.24815572 -0.24202679 -0.23192379 -0.21801260 -0.20052166
## [40,] -0.22436448 -0.22252245 -0.21702661 -0.20796720 -0.19549297 -0.17980875
## [41,] -0.20200763 -0.20034915 -0.19540094 -0.18724425 -0.17601302 -0.16189166
## [42,] -0.18259945 -0.18110031 -0.17662751 -0.16925449 -0.15910231 -0.14633769
## [43,] -0.16568601 -0.16432573 -0.16026723 -0.15357714 -0.14436532 -0.13278303
## [44,] -0.15088778 -0.14964899 -0.14595297 -0.13986041 -0.13147134 -0.12092352
## [45,] -0.13788811 -0.13675606 -0.13337846 -0.12781080 -0.12014449 -0.11050541
## [46,] -0.12642295 -0.12538502 -0.12228827 -0.11718355 -0.11015468 -0.10131707
## [47,] -0.11627176 -0.11531717 -0.11246907 -0.10777424 -0.10130976 -0.09318177
## [48,] -0.10724999 -0.10636947 -0.10374236 -0.09941181 -0.09344892 -0.08595160
## [49,] -0.09920276 -0.09838830 -0.09595832 -0.09195270 -0.08643722 -0.07950244
## [50,] -0.09199967 -0.09124435 -0.08899081 -0.08527603 -0.08016103 -0.07372979
##              [,7]        [,8]        [,9]       [,10]       [,11]       [,12]
##  [1,] -0.06608790 -0.05736085 -0.04769194 -0.03723993 -0.02617644 -0.01468314
##  [2,] -0.07126224 -0.06185191 -0.05142597 -0.04015562 -0.02822592 -0.01583275
##  [3,] -0.07704296 -0.06686927 -0.05559760 -0.04341301 -0.03051558 -0.01711709
##  [4,] -0.08352374 -0.07249426 -0.06027442 -0.04706487 -0.03308252 -0.01855696
##  [5,] -0.09081584 -0.07882342 -0.06553672 -0.05117390 -0.03597082 -0.02017709
##  [6,] -0.09905184 -0.08597183 -0.07148017 -0.05581481 -0.03923297 -0.02200693
##  [7,] -0.10839014 -0.09407699 -0.07821910 -0.06107686 -0.04293173 -0.02408167
##  [8,] -0.11902044 -0.10330354 -0.08589040 -0.06706694 -0.04714224 -0.02644347
##  [9,] -0.13117020 -0.11384889 -0.09465820 -0.07391322 -0.05195458 -0.02914285
## [10,] -0.14511205 -0.12594970 -0.10471925 -0.08176932 -0.05747674 -0.03224040
## [11,] -0.16117208 -0.13988897 -0.11630888 -0.09081901 -0.06383788 -0.03580855
## [12,] -0.17973815 -0.15600335 -0.12970697 -0.10128082 -0.07119163 -0.03993348
## [13,] -0.20126685 -0.17468913 -0.14524303 -0.11341204 -0.07971883 -0.04471664
## [14,] -0.22628603 -0.19640448 -0.16329798 -0.12751012 -0.08962856 -0.05027530
## [15,] -0.25538727 -0.22166284 -0.18429872 -0.14390841 -0.10115513 -0.05674089
## [16,] -0.28919816 -0.25100894 -0.20869815 -0.16296054 -0.11454713 -0.06425285
## [17,] -0.32831775 -0.28496270 -0.23692857 -0.18500408 -0.13004182 -0.07294428
## [18,] -0.37318981 -0.32390931 -0.26931022 -0.21028907 -0.14781498 -0.08291377
## [19,] -0.42388115 -0.36790675 -0.30589133 -0.23885319 -0.16789308 -0.09417617
## [20,] -0.47973581 -0.41638568 -0.34619851 -0.27032678 -0.19001628 -0.10658572
## [21,] -0.53891274 -0.46774818 -0.38890320 -0.30367244 -0.21345539 -0.11973341
## [22,] -0.59791668 -0.51896052 -0.43148304 -0.33692062 -0.23682598 -0.13284266
## [23,] -0.65140713 -0.56538744 -0.47008411 -0.36706201 -0.25801276 -0.14472695
## [24,] -0.69272169 -0.60124633 -0.49989852 -0.39034239 -0.27437685 -0.15390605
## [25,] -0.71540858 -0.62093736 -0.51627038 -0.40312624 -0.28336279 -0.15894653
## [26,] -0.71540858 -0.62093736 -0.51627038 -0.40312624 -0.28336279 -0.15894653
## [27,] -0.69272169 -0.60124633 -0.49989852 -0.39034239 -0.27437685 -0.15390605
## [28,] -0.65140713 -0.56538744 -0.47008411 -0.36706201 -0.25801276 -0.14472695
## [29,] -0.59791668 -0.51896052 -0.43148304 -0.33692062 -0.23682598 -0.13284266
## [30,] -0.53891274 -0.46774818 -0.38890320 -0.30367244 -0.21345539 -0.11973341
## [31,] -0.47973581 -0.41638568 -0.34619851 -0.27032678 -0.19001628 -0.10658572
## [32,] -0.42388115 -0.36790675 -0.30589133 -0.23885319 -0.16789308 -0.09417617
## [33,] -0.37318981 -0.32390931 -0.26931022 -0.21028907 -0.14781498 -0.08291377
## [34,] -0.32831775 -0.28496270 -0.23692857 -0.18500408 -0.13004182 -0.07294428
## [35,] -0.28919816 -0.25100894 -0.20869815 -0.16296054 -0.11454713 -0.06425285
## [36,] -0.25538727 -0.22166284 -0.18429872 -0.14390841 -0.10115513 -0.05674089
## [37,] -0.22628603 -0.19640448 -0.16329798 -0.12751012 -0.08962856 -0.05027530
## [38,] -0.20126685 -0.17468913 -0.14524303 -0.11341204 -0.07971883 -0.04471664
## [39,] -0.17973815 -0.15600335 -0.12970697 -0.10128082 -0.07119163 -0.03993348
## [40,] -0.16117208 -0.13988897 -0.11630888 -0.09081901 -0.06383788 -0.03580855
## [41,] -0.14511205 -0.12594970 -0.10471925 -0.08176932 -0.05747674 -0.03224040
## [42,] -0.13117020 -0.11384889 -0.09465820 -0.07391322 -0.05195458 -0.02914285
## [43,] -0.11902044 -0.10330354 -0.08589040 -0.06706694 -0.04714224 -0.02644347
## [44,] -0.10839014 -0.09407699 -0.07821910 -0.06107686 -0.04293173 -0.02408167
## [45,] -0.09905184 -0.08597183 -0.07148017 -0.05581481 -0.03923297 -0.02200693
## [46,] -0.09081584 -0.07882342 -0.06553672 -0.05117390 -0.03597082 -0.02017709
## [47,] -0.08352374 -0.07249426 -0.06027442 -0.04706487 -0.03308252 -0.01855696
## [48,] -0.07704296 -0.06686927 -0.05559760 -0.04341301 -0.03051558 -0.01711709
## [49,] -0.07126224 -0.06185191 -0.05142597 -0.04015562 -0.02822592 -0.01583275
## [50,] -0.06608790 -0.05736085 -0.04769194 -0.03723993 -0.02617644 -0.01468314
##              [,13]       [,14]      [,15]      [,16]      [,17]      [,18]
##  [1,] -0.002948735 0.008834087 0.02047185 0.03177347 0.04255337 0.05263454
##  [2,] -0.003179605 0.009525749 0.02207469 0.03426117 0.04588507 0.05675555
##  [3,] -0.003437531 0.010298468 0.02386537 0.03704040 0.04960723 0.06135950
##  [4,] -0.003726693 0.011164766 0.02587290 0.04015620 0.05378014 0.06652101
##  [5,] -0.004052055 0.012139514 0.02813175 0.04366207 0.05847545 0.07232868
##  [6,] -0.004419532 0.013240434 0.03068299 0.04762174 0.06377853 0.07888809
##  [7,] -0.004836191 0.014488701 0.03357569 0.05211137 0.06979137 0.08632541
##  [8,] -0.005310498 0.015909672 0.03686861 0.05722216 0.07663613 0.09479173
##  [9,] -0.005852600 0.017533752 0.04063220 0.06306347 0.08445924 0.10446819
## [10,] -0.006474663 0.019397384 0.04495093 0.06976638 0.09343626 0.11557193
## [11,] -0.007191236 0.021544156 0.04992579 0.07748765 0.10377716 0.12836266
## [12,] -0.008019623 0.024025916 0.05567695 0.08641377 0.11573168 0.14314928
## [13,] -0.008980199 0.026903695 0.06234583 0.09676425 0.12959380 0.16029543
## [14,] -0.010096514 0.030248053 0.07009595 0.10879287 0.14570341 0.18022151
## [15,] -0.011394964 0.034138067 0.07911055 0.12278404 0.16444143 0.20339868
## [16,] -0.012903551 0.038657629 0.08958405 0.13903951 0.18621194 0.23032677
## [17,] -0.014649003 0.043886814 0.10170201 0.15784726 0.21140067 0.26148288
## [18,] -0.016651121 0.049884941 0.11560189 0.17942067 0.24029336 0.29722044
## [19,] -0.018912886 0.056660942 0.13130440 0.20379184 0.27293303 0.33759266
## [20,] -0.021405030 0.064127132 0.14860633 0.23064541 0.30889731 0.38207712
## [21,] -0.024045408 0.072037417 0.16693739 0.25909626 0.34700077 0.42920754
## [22,] -0.026678068 0.079924578 0.18521486 0.28746393 0.38499284 0.47620018
## [23,] -0.029064725 0.087074741 0.20178444 0.31318085 0.41943483 0.51880171
## [24,] -0.030908113 0.092597332 0.21458233 0.33304390 0.44603689 0.55170597
## [25,] -0.031920365 0.095629927 0.22160998 0.34395120 0.46064475 0.56977453
## [26,] -0.031920365 0.095629927 0.22160998 0.34395120 0.46064475 0.56977453
## [27,] -0.030908113 0.092597332 0.21458233 0.33304390 0.44603689 0.55170597
## [28,] -0.029064725 0.087074741 0.20178444 0.31318085 0.41943483 0.51880171
## [29,] -0.026678068 0.079924578 0.18521486 0.28746393 0.38499284 0.47620018
## [30,] -0.024045408 0.072037417 0.16693739 0.25909626 0.34700077 0.42920754
## [31,] -0.021405030 0.064127132 0.14860633 0.23064541 0.30889731 0.38207712
## [32,] -0.018912886 0.056660942 0.13130440 0.20379184 0.27293303 0.33759266
## [33,] -0.016651121 0.049884941 0.11560189 0.17942067 0.24029336 0.29722044
## [34,] -0.014649003 0.043886814 0.10170201 0.15784726 0.21140067 0.26148288
## [35,] -0.012903551 0.038657629 0.08958405 0.13903951 0.18621194 0.23032677
## [36,] -0.011394964 0.034138067 0.07911055 0.12278404 0.16444143 0.20339868
## [37,] -0.010096514 0.030248053 0.07009595 0.10879287 0.14570341 0.18022151
## [38,] -0.008980199 0.026903695 0.06234583 0.09676425 0.12959380 0.16029543
## [39,] -0.008019623 0.024025916 0.05567695 0.08641377 0.11573168 0.14314928
## [40,] -0.007191236 0.021544156 0.04992579 0.07748765 0.10377716 0.12836266
## [41,] -0.006474663 0.019397384 0.04495093 0.06976638 0.09343626 0.11557193
## [42,] -0.005852600 0.017533752 0.04063220 0.06306347 0.08445924 0.10446819
## [43,] -0.005310498 0.015909672 0.03686861 0.05722216 0.07663613 0.09479173
## [44,] -0.004836191 0.014488701 0.03357569 0.05211137 0.06979137 0.08632541
## [45,] -0.004419532 0.013240434 0.03068299 0.04762174 0.06377853 0.07888809
## [46,] -0.004052055 0.012139514 0.02813175 0.04366207 0.05847545 0.07232868
## [47,] -0.003726693 0.011164766 0.02587290 0.04015620 0.05378014 0.06652101
## [48,] -0.003437531 0.010298468 0.02386537 0.03704040 0.04960723 0.06135950
## [49,] -0.003179605 0.009525749 0.02207469 0.03426117 0.04588507 0.05675555
## [50,] -0.002948735 0.008834087 0.02047185 0.03177347 0.04255337 0.05263454
##            [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
##  [1,] 0.06185146 0.07005278 0.07710383 0.08288884 0.08731281 0.09030312
##  [2,] 0.06669410 0.07553754 0.08314065 0.08937860 0.09414895 0.09737338
##  [3,] 0.07210426 0.08166507 0.08988494 0.09662890 0.10178622 0.10527221
##  [4,] 0.07816961 0.08853466 0.09744598 0.10475723 0.11034838 0.11412761
##  [5,] 0.08499426 0.09626424 0.10595357 0.11390314 0.11998243 0.12409160
##  [6,] 0.09270230 0.10499435 0.11556239 0.12423290 0.13086351 0.13534534
##  [7,] 0.10144199 0.11489289 0.12645725 0.13594519 0.14320091 0.14810528
##  [8,] 0.11139085 0.12616095 0.13885948 0.14927794 0.15724526 0.16263062
##  [9,] 0.12276177 0.13903961 0.15303443 0.16451642 0.17329706 0.17923216
## [10,] 0.13580991 0.15381789 0.16930019 0.18200258 0.19171650 0.19828244
## [11,] 0.15084044 0.17084143 0.18803720 0.20214541 0.21293440 0.22022701
## [12,] 0.16821637 0.19052135 0.20969798 0.22543137 0.23746318 0.24559586
## [13,] 0.18836501 0.21334164 0.23481520 0.25243311 0.26590608 0.27501287
## [14,] 0.21178038 0.23986182 0.26400473 0.28381270 0.29896046 0.30919931
## [15,] 0.23901614 0.27070896 0.29795674 0.32031209 0.33740791 0.34896351
## [16,] 0.27065965 0.30654830 0.33740344 0.36271842 0.38207758 0.39516303
## [17,] 0.30727155 0.34801483 0.38304371 0.41178303 0.43376088 0.44861639
## [18,] 0.34926717 0.39557894 0.43539531 0.46806251 0.49304414 0.50992999
## [19,] 0.39670903 0.44931145 0.49453619 0.53164066 0.56001560 0.57919511
## [20,] 0.44898323 0.50851705 0.55970103 0.60169474 0.63380864 0.65551542
## [21,] 0.50436673 0.57124424 0.62874193 0.67591570 0.71199095 0.73637532
## [22,] 0.55958833 0.63378805 0.69758099 0.74991967 0.78994469 0.81699884
## [23,] 0.60964988 0.69048761 0.75998756 0.81700853 0.86061424 0.89008869
## [24,] 0.64831605 0.73428080 0.80818868 0.86882612 0.91519747 0.94654129
## [25,] 0.66954863 0.75832876 0.83465714 0.89728049 0.94517051 0.97754086
## [26,] 0.66954863 0.75832876 0.83465714 0.89728049 0.94517051 0.97754086
## [27,] 0.64831605 0.73428080 0.80818868 0.86882612 0.91519747 0.94654129
## [28,] 0.60964988 0.69048761 0.75998756 0.81700853 0.86061424 0.89008869
## [29,] 0.55958833 0.63378805 0.69758099 0.74991967 0.78994469 0.81699884
## [30,] 0.50436673 0.57124424 0.62874193 0.67591570 0.71199095 0.73637532
## [31,] 0.44898323 0.50851705 0.55970103 0.60169474 0.63380864 0.65551542
## [32,] 0.39670903 0.44931145 0.49453619 0.53164066 0.56001560 0.57919511
## [33,] 0.34926717 0.39557894 0.43539531 0.46806251 0.49304414 0.50992999
## [34,] 0.30727155 0.34801483 0.38304371 0.41178303 0.43376088 0.44861639
## [35,] 0.27065965 0.30654830 0.33740344 0.36271842 0.38207758 0.39516303
## [36,] 0.23901614 0.27070896 0.29795674 0.32031209 0.33740791 0.34896351
## [37,] 0.21178038 0.23986182 0.26400473 0.28381270 0.29896046 0.30919931
## [38,] 0.18836501 0.21334164 0.23481520 0.25243311 0.26590608 0.27501287
## [39,] 0.16821637 0.19052135 0.20969798 0.22543137 0.23746318 0.24559586
## [40,] 0.15084044 0.17084143 0.18803720 0.20214541 0.21293440 0.22022701
## [41,] 0.13580991 0.15381789 0.16930019 0.18200258 0.19171650 0.19828244
## [42,] 0.12276177 0.13903961 0.15303443 0.16451642 0.17329706 0.17923216
## [43,] 0.11139085 0.12616095 0.13885948 0.14927794 0.15724526 0.16263062
## [44,] 0.10144199 0.11489289 0.12645725 0.13594519 0.14320091 0.14810528
## [45,] 0.09270230 0.10499435 0.11556239 0.12423290 0.13086351 0.13534534
## [46,] 0.08499426 0.09626424 0.10595357 0.11390314 0.11998243 0.12409160
## [47,] 0.07816961 0.08853466 0.09744598 0.10475723 0.11034838 0.11412761
## [48,] 0.07210426 0.08166507 0.08988494 0.09662890 0.10178622 0.10527221
## [49,] 0.06669410 0.07553754 0.08314065 0.08937860 0.09414895 0.09737338
## [50,] 0.06185146 0.07005278 0.07710383 0.08288884 0.08731281 0.09030312
##            [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
##  [1,] 0.09181065 0.09181065 0.09030312 0.08731281 0.08288884 0.07710383
##  [2,] 0.09899894 0.09899894 0.09737338 0.09414895 0.08937860 0.08314065
##  [3,] 0.10702963 0.10702963 0.10527221 0.10178622 0.09662890 0.08988494
##  [4,] 0.11603286 0.11603286 0.11412761 0.11034838 0.10475723 0.09744598
##  [5,] 0.12616320 0.12616320 0.12409160 0.11998243 0.11390314 0.10595357
##  [6,] 0.13760481 0.13760481 0.13534534 0.13086351 0.12423290 0.11556239
##  [7,] 0.15057776 0.15057776 0.14810528 0.14320091 0.13594519 0.12645725
##  [8,] 0.16534559 0.16534559 0.16263062 0.15724526 0.14927794 0.13885948
##  [9,] 0.18222428 0.18222428 0.17923216 0.17329706 0.16451642 0.15303443
## [10,] 0.20159258 0.20159258 0.19828244 0.19171650 0.18200258 0.16930019
## [11,] 0.22390350 0.22390350 0.22022701 0.21293440 0.20214541 0.18803720
## [12,] 0.24969586 0.24969586 0.24559586 0.23746318 0.22543137 0.20969798
## [13,] 0.27960396 0.27960396 0.27501287 0.26590608 0.25243311 0.23481520
## [14,] 0.31436111 0.31436111 0.30919931 0.29896046 0.28381270 0.26400473
## [15,] 0.35478914 0.35478914 0.34896351 0.33740791 0.32031209 0.29795674
## [16,] 0.40175992 0.40175992 0.39516303 0.38207758 0.36271842 0.33740344
## [17,] 0.45610564 0.45610564 0.44861639 0.43376088 0.41178303 0.38304371
## [18,] 0.51844281 0.51844281 0.50992999 0.49304414 0.46806251 0.43539531
## [19,] 0.58886424 0.58886424 0.57919511 0.56001560 0.53164066 0.49453619
## [20,] 0.66645865 0.66645865 0.65551542 0.63380864 0.60169474 0.55970103
## [21,] 0.74866844 0.74866844 0.73637532 0.71199095 0.67591570 0.62874193
## [22,] 0.83063789 0.83063789 0.81699884 0.78994469 0.74991967 0.69758099
## [23,] 0.90494791 0.90494791 0.89008869 0.86061424 0.81700853 0.75998756
## [24,] 0.96234294 0.96234294 0.94654129 0.91519747 0.86882612 0.80818868
## [25,] 0.99386001 0.99386001 0.97754086 0.94517051 0.89728049 0.83465714
## [26,] 0.99386001 0.99386001 0.97754086 0.94517051 0.89728049 0.83465714
## [27,] 0.96234294 0.96234294 0.94654129 0.91519747 0.86882612 0.80818868
## [28,] 0.90494791 0.90494791 0.89008869 0.86061424 0.81700853 0.75998756
## [29,] 0.83063789 0.83063789 0.81699884 0.78994469 0.74991967 0.69758099
## [30,] 0.74866844 0.74866844 0.73637532 0.71199095 0.67591570 0.62874193
## [31,] 0.66645865 0.66645865 0.65551542 0.63380864 0.60169474 0.55970103
## [32,] 0.58886424 0.58886424 0.57919511 0.56001560 0.53164066 0.49453619
## [33,] 0.51844281 0.51844281 0.50992999 0.49304414 0.46806251 0.43539531
## [34,] 0.45610564 0.45610564 0.44861639 0.43376088 0.41178303 0.38304371
## [35,] 0.40175992 0.40175992 0.39516303 0.38207758 0.36271842 0.33740344
## [36,] 0.35478914 0.35478914 0.34896351 0.33740791 0.32031209 0.29795674
## [37,] 0.31436111 0.31436111 0.30919931 0.29896046 0.28381270 0.26400473
## [38,] 0.27960396 0.27960396 0.27501287 0.26590608 0.25243311 0.23481520
## [39,] 0.24969586 0.24969586 0.24559586 0.23746318 0.22543137 0.20969798
## [40,] 0.22390350 0.22390350 0.22022701 0.21293440 0.20214541 0.18803720
## [41,] 0.20159258 0.20159258 0.19828244 0.19171650 0.18200258 0.16930019
## [42,] 0.18222428 0.18222428 0.17923216 0.17329706 0.16451642 0.15303443
## [43,] 0.16534559 0.16534559 0.16263062 0.15724526 0.14927794 0.13885948
## [44,] 0.15057776 0.15057776 0.14810528 0.14320091 0.13594519 0.12645725
## [45,] 0.13760481 0.13760481 0.13534534 0.13086351 0.12423290 0.11556239
## [46,] 0.12616320 0.12616320 0.12409160 0.11998243 0.11390314 0.10595357
## [47,] 0.11603286 0.11603286 0.11412761 0.11034838 0.10475723 0.09744598
## [48,] 0.10702963 0.10702963 0.10527221 0.10178622 0.09662890 0.08988494
## [49,] 0.09899894 0.09899894 0.09737338 0.09414895 0.08937860 0.08314065
## [50,] 0.09181065 0.09181065 0.09030312 0.08731281 0.08288884 0.07710383
##            [,31]      [,32]      [,33]      [,34]      [,35]      [,36]
##  [1,] 0.07005278 0.06185146 0.05263454 0.04255337 0.03177347 0.02047185
##  [2,] 0.07553754 0.06669410 0.05675555 0.04588507 0.03426117 0.02207469
##  [3,] 0.08166507 0.07210426 0.06135950 0.04960723 0.03704040 0.02386537
##  [4,] 0.08853466 0.07816961 0.06652101 0.05378014 0.04015620 0.02587290
##  [5,] 0.09626424 0.08499426 0.07232868 0.05847545 0.04366207 0.02813175
##  [6,] 0.10499435 0.09270230 0.07888809 0.06377853 0.04762174 0.03068299
##  [7,] 0.11489289 0.10144199 0.08632541 0.06979137 0.05211137 0.03357569
##  [8,] 0.12616095 0.11139085 0.09479173 0.07663613 0.05722216 0.03686861
##  [9,] 0.13903961 0.12276177 0.10446819 0.08445924 0.06306347 0.04063220
## [10,] 0.15381789 0.13580991 0.11557193 0.09343626 0.06976638 0.04495093
## [11,] 0.17084143 0.15084044 0.12836266 0.10377716 0.07748765 0.04992579
## [12,] 0.19052135 0.16821637 0.14314928 0.11573168 0.08641377 0.05567695
## [13,] 0.21334164 0.18836501 0.16029543 0.12959380 0.09676425 0.06234583
## [14,] 0.23986182 0.21178038 0.18022151 0.14570341 0.10879287 0.07009595
## [15,] 0.27070896 0.23901614 0.20339868 0.16444143 0.12278404 0.07911055
## [16,] 0.30654830 0.27065965 0.23032677 0.18621194 0.13903951 0.08958405
## [17,] 0.34801483 0.30727155 0.26148288 0.21140067 0.15784726 0.10170201
## [18,] 0.39557894 0.34926717 0.29722044 0.24029336 0.17942067 0.11560189
## [19,] 0.44931145 0.39670903 0.33759266 0.27293303 0.20379184 0.13130440
## [20,] 0.50851705 0.44898323 0.38207712 0.30889731 0.23064541 0.14860633
## [21,] 0.57124424 0.50436673 0.42920754 0.34700077 0.25909626 0.16693739
## [22,] 0.63378805 0.55958833 0.47620018 0.38499284 0.28746393 0.18521486
## [23,] 0.69048761 0.60964988 0.51880171 0.41943483 0.31318085 0.20178444
## [24,] 0.73428080 0.64831605 0.55170597 0.44603689 0.33304390 0.21458233
## [25,] 0.75832876 0.66954863 0.56977453 0.46064475 0.34395120 0.22160998
## [26,] 0.75832876 0.66954863 0.56977453 0.46064475 0.34395120 0.22160998
## [27,] 0.73428080 0.64831605 0.55170597 0.44603689 0.33304390 0.21458233
## [28,] 0.69048761 0.60964988 0.51880171 0.41943483 0.31318085 0.20178444
## [29,] 0.63378805 0.55958833 0.47620018 0.38499284 0.28746393 0.18521486
## [30,] 0.57124424 0.50436673 0.42920754 0.34700077 0.25909626 0.16693739
## [31,] 0.50851705 0.44898323 0.38207712 0.30889731 0.23064541 0.14860633
## [32,] 0.44931145 0.39670903 0.33759266 0.27293303 0.20379184 0.13130440
## [33,] 0.39557894 0.34926717 0.29722044 0.24029336 0.17942067 0.11560189
## [34,] 0.34801483 0.30727155 0.26148288 0.21140067 0.15784726 0.10170201
## [35,] 0.30654830 0.27065965 0.23032677 0.18621194 0.13903951 0.08958405
## [36,] 0.27070896 0.23901614 0.20339868 0.16444143 0.12278404 0.07911055
## [37,] 0.23986182 0.21178038 0.18022151 0.14570341 0.10879287 0.07009595
## [38,] 0.21334164 0.18836501 0.16029543 0.12959380 0.09676425 0.06234583
## [39,] 0.19052135 0.16821637 0.14314928 0.11573168 0.08641377 0.05567695
## [40,] 0.17084143 0.15084044 0.12836266 0.10377716 0.07748765 0.04992579
## [41,] 0.15381789 0.13580991 0.11557193 0.09343626 0.06976638 0.04495093
## [42,] 0.13903961 0.12276177 0.10446819 0.08445924 0.06306347 0.04063220
## [43,] 0.12616095 0.11139085 0.09479173 0.07663613 0.05722216 0.03686861
## [44,] 0.11489289 0.10144199 0.08632541 0.06979137 0.05211137 0.03357569
## [45,] 0.10499435 0.09270230 0.07888809 0.06377853 0.04762174 0.03068299
## [46,] 0.09626424 0.08499426 0.07232868 0.05847545 0.04366207 0.02813175
## [47,] 0.08853466 0.07816961 0.06652101 0.05378014 0.04015620 0.02587290
## [48,] 0.08166507 0.07210426 0.06135950 0.04960723 0.03704040 0.02386537
## [49,] 0.07553754 0.06669410 0.05675555 0.04588507 0.03426117 0.02207469
## [50,] 0.07005278 0.06185146 0.05263454 0.04255337 0.03177347 0.02047185
##             [,37]        [,38]       [,39]       [,40]       [,41]       [,42]
##  [1,] 0.008834087 -0.002948735 -0.01468314 -0.02617644 -0.03723993 -0.04769194
##  [2,] 0.009525749 -0.003179605 -0.01583275 -0.02822592 -0.04015562 -0.05142597
##  [3,] 0.010298468 -0.003437531 -0.01711709 -0.03051558 -0.04341301 -0.05559760
##  [4,] 0.011164766 -0.003726693 -0.01855696 -0.03308252 -0.04706487 -0.06027442
##  [5,] 0.012139514 -0.004052055 -0.02017709 -0.03597082 -0.05117390 -0.06553672
##  [6,] 0.013240434 -0.004419532 -0.02200693 -0.03923297 -0.05581481 -0.07148017
##  [7,] 0.014488701 -0.004836191 -0.02408167 -0.04293173 -0.06107686 -0.07821910
##  [8,] 0.015909672 -0.005310498 -0.02644347 -0.04714224 -0.06706694 -0.08589040
##  [9,] 0.017533752 -0.005852600 -0.02914285 -0.05195458 -0.07391322 -0.09465820
## [10,] 0.019397384 -0.006474663 -0.03224040 -0.05747674 -0.08176932 -0.10471925
## [11,] 0.021544156 -0.007191236 -0.03580855 -0.06383788 -0.09081901 -0.11630888
## [12,] 0.024025916 -0.008019623 -0.03993348 -0.07119163 -0.10128082 -0.12970697
## [13,] 0.026903695 -0.008980199 -0.04471664 -0.07971883 -0.11341204 -0.14524303
## [14,] 0.030248053 -0.010096514 -0.05027530 -0.08962856 -0.12751012 -0.16329798
## [15,] 0.034138067 -0.011394964 -0.05674089 -0.10115513 -0.14390841 -0.18429872
## [16,] 0.038657629 -0.012903551 -0.06425285 -0.11454713 -0.16296054 -0.20869815
## [17,] 0.043886814 -0.014649003 -0.07294428 -0.13004182 -0.18500408 -0.23692857
## [18,] 0.049884941 -0.016651121 -0.08291377 -0.14781498 -0.21028907 -0.26931022
## [19,] 0.056660942 -0.018912886 -0.09417617 -0.16789308 -0.23885319 -0.30589133
## [20,] 0.064127132 -0.021405030 -0.10658572 -0.19001628 -0.27032678 -0.34619851
## [21,] 0.072037417 -0.024045408 -0.11973341 -0.21345539 -0.30367244 -0.38890320
## [22,] 0.079924578 -0.026678068 -0.13284266 -0.23682598 -0.33692062 -0.43148304
## [23,] 0.087074741 -0.029064725 -0.14472695 -0.25801276 -0.36706201 -0.47008411
## [24,] 0.092597332 -0.030908113 -0.15390605 -0.27437685 -0.39034239 -0.49989852
## [25,] 0.095629927 -0.031920365 -0.15894653 -0.28336279 -0.40312624 -0.51627038
## [26,] 0.095629927 -0.031920365 -0.15894653 -0.28336279 -0.40312624 -0.51627038
## [27,] 0.092597332 -0.030908113 -0.15390605 -0.27437685 -0.39034239 -0.49989852
## [28,] 0.087074741 -0.029064725 -0.14472695 -0.25801276 -0.36706201 -0.47008411
## [29,] 0.079924578 -0.026678068 -0.13284266 -0.23682598 -0.33692062 -0.43148304
## [30,] 0.072037417 -0.024045408 -0.11973341 -0.21345539 -0.30367244 -0.38890320
## [31,] 0.064127132 -0.021405030 -0.10658572 -0.19001628 -0.27032678 -0.34619851
## [32,] 0.056660942 -0.018912886 -0.09417617 -0.16789308 -0.23885319 -0.30589133
## [33,] 0.049884941 -0.016651121 -0.08291377 -0.14781498 -0.21028907 -0.26931022
## [34,] 0.043886814 -0.014649003 -0.07294428 -0.13004182 -0.18500408 -0.23692857
## [35,] 0.038657629 -0.012903551 -0.06425285 -0.11454713 -0.16296054 -0.20869815
## [36,] 0.034138067 -0.011394964 -0.05674089 -0.10115513 -0.14390841 -0.18429872
## [37,] 0.030248053 -0.010096514 -0.05027530 -0.08962856 -0.12751012 -0.16329798
## [38,] 0.026903695 -0.008980199 -0.04471664 -0.07971883 -0.11341204 -0.14524303
## [39,] 0.024025916 -0.008019623 -0.03993348 -0.07119163 -0.10128082 -0.12970697
## [40,] 0.021544156 -0.007191236 -0.03580855 -0.06383788 -0.09081901 -0.11630888
## [41,] 0.019397384 -0.006474663 -0.03224040 -0.05747674 -0.08176932 -0.10471925
## [42,] 0.017533752 -0.005852600 -0.02914285 -0.05195458 -0.07391322 -0.09465820
## [43,] 0.015909672 -0.005310498 -0.02644347 -0.04714224 -0.06706694 -0.08589040
## [44,] 0.014488701 -0.004836191 -0.02408167 -0.04293173 -0.06107686 -0.07821910
## [45,] 0.013240434 -0.004419532 -0.02200693 -0.03923297 -0.05581481 -0.07148017
## [46,] 0.012139514 -0.004052055 -0.02017709 -0.03597082 -0.05117390 -0.06553672
## [47,] 0.011164766 -0.003726693 -0.01855696 -0.03308252 -0.04706487 -0.06027442
## [48,] 0.010298468 -0.003437531 -0.01711709 -0.03051558 -0.04341301 -0.05559760
## [49,] 0.009525749 -0.003179605 -0.01583275 -0.02822592 -0.04015562 -0.05142597
## [50,] 0.008834087 -0.002948735 -0.01468314 -0.02617644 -0.03723993 -0.04769194
##             [,43]       [,44]       [,45]       [,46]       [,47]       [,48]
##  [1,] -0.05736085 -0.06608790 -0.07372979 -0.08016103 -0.08527603 -0.08899081
##  [2,] -0.06185191 -0.07126224 -0.07950244 -0.08643722 -0.09195270 -0.09595832
##  [3,] -0.06686927 -0.07704296 -0.08595160 -0.09344892 -0.09941181 -0.10374236
##  [4,] -0.07249426 -0.08352374 -0.09318177 -0.10130976 -0.10777424 -0.11246907
##  [5,] -0.07882342 -0.09081584 -0.10131707 -0.11015468 -0.11718355 -0.12228827
##  [6,] -0.08597183 -0.09905184 -0.11050541 -0.12014449 -0.12781080 -0.13337846
##  [7,] -0.09407699 -0.10839014 -0.12092352 -0.13147134 -0.13986041 -0.14595297
##  [8,] -0.10330354 -0.11902044 -0.13278303 -0.14436532 -0.15357714 -0.16026723
##  [9,] -0.11384889 -0.13117020 -0.14633769 -0.15910231 -0.16925449 -0.17662751
## [10,] -0.12594970 -0.14511205 -0.16189166 -0.17601302 -0.18724425 -0.19540094
## [11,] -0.13988897 -0.16117208 -0.17980875 -0.19549297 -0.20796720 -0.21702661
## [12,] -0.15600335 -0.17973815 -0.20052166 -0.21801260 -0.23192379 -0.24202679
## [13,] -0.17468913 -0.20126685 -0.22453976 -0.24412574 -0.25970318 -0.27101630
## [14,] -0.19640448 -0.22628603 -0.25245196 -0.27447265 -0.29198650 -0.30470594
## [15,] -0.22166284 -0.25538727 -0.28491825 -0.30977087 -0.32953707 -0.34389228
## [16,] -0.25100894 -0.28919816 -0.32263877 -0.35078165 -0.37316471 -0.38942041
## [17,] -0.28496270 -0.32831775 -0.36628184 -0.39823158 -0.42364238 -0.44209697
## [18,] -0.32390931 -0.37318981 -0.41634255 -0.45265895 -0.48154270 -0.50251954
## [19,] -0.36790675 -0.42388115 -0.47289544 -0.51414479 -0.54695190 -0.57077808
## [20,] -0.41638568 -0.47973581 -0.53520868 -0.58189345 -0.61902354 -0.64598928
## [21,] -0.46774818 -0.53891274 -0.60122837 -0.65367185 -0.69538206 -0.72567411
## [22,] -0.51896052 -0.59791668 -0.66705506 -0.72524042 -0.77151735 -0.80512599
## [23,] -0.56538744 -0.65140713 -0.72673073 -0.79012143 -0.84053836 -0.87715367
## [24,] -0.60124633 -0.69272169 -0.77282259 -0.84023375 -0.89384830 -0.93278589
## [25,] -0.62093736 -0.71540858 -0.79813280 -0.86775170 -0.92312215 -0.96333496
## [26,] -0.62093736 -0.71540858 -0.79813280 -0.86775170 -0.92312215 -0.96333496
## [27,] -0.60124633 -0.69272169 -0.77282259 -0.84023375 -0.89384830 -0.93278589
## [28,] -0.56538744 -0.65140713 -0.72673073 -0.79012143 -0.84053836 -0.87715367
## [29,] -0.51896052 -0.59791668 -0.66705506 -0.72524042 -0.77151735 -0.80512599
## [30,] -0.46774818 -0.53891274 -0.60122837 -0.65367185 -0.69538206 -0.72567411
## [31,] -0.41638568 -0.47973581 -0.53520868 -0.58189345 -0.61902354 -0.64598928
## [32,] -0.36790675 -0.42388115 -0.47289544 -0.51414479 -0.54695190 -0.57077808
## [33,] -0.32390931 -0.37318981 -0.41634255 -0.45265895 -0.48154270 -0.50251954
## [34,] -0.28496270 -0.32831775 -0.36628184 -0.39823158 -0.42364238 -0.44209697
## [35,] -0.25100894 -0.28919816 -0.32263877 -0.35078165 -0.37316471 -0.38942041
## [36,] -0.22166284 -0.25538727 -0.28491825 -0.30977087 -0.32953707 -0.34389228
## [37,] -0.19640448 -0.22628603 -0.25245196 -0.27447265 -0.29198650 -0.30470594
## [38,] -0.17468913 -0.20126685 -0.22453976 -0.24412574 -0.25970318 -0.27101630
## [39,] -0.15600335 -0.17973815 -0.20052166 -0.21801260 -0.23192379 -0.24202679
## [40,] -0.13988897 -0.16117208 -0.17980875 -0.19549297 -0.20796720 -0.21702661
## [41,] -0.12594970 -0.14511205 -0.16189166 -0.17601302 -0.18724425 -0.19540094
## [42,] -0.11384889 -0.13117020 -0.14633769 -0.15910231 -0.16925449 -0.17662751
## [43,] -0.10330354 -0.11902044 -0.13278303 -0.14436532 -0.15357714 -0.16026723
## [44,] -0.09407699 -0.10839014 -0.12092352 -0.13147134 -0.13986041 -0.14595297
## [45,] -0.08597183 -0.09905184 -0.11050541 -0.12014449 -0.12781080 -0.13337846
## [46,] -0.07882342 -0.09081584 -0.10131707 -0.11015468 -0.11718355 -0.12228827
## [47,] -0.07249426 -0.08352374 -0.09318177 -0.10130976 -0.10777424 -0.11246907
## [48,] -0.06686927 -0.07704296 -0.08595160 -0.09344892 -0.09941181 -0.10374236
## [49,] -0.06185191 -0.07126224 -0.07950244 -0.08643722 -0.09195270 -0.09595832
## [50,] -0.05736085 -0.06608790 -0.07372979 -0.08016103 -0.08527603 -0.08899081
##             [,49]       [,50]
##  [1,] -0.09124435 -0.09199967
##  [2,] -0.09838830 -0.09920276
##  [3,] -0.10636947 -0.10724999
##  [4,] -0.11531717 -0.11627176
##  [5,] -0.12538502 -0.12642295
##  [6,] -0.13675606 -0.13788811
##  [7,] -0.14964899 -0.15088778
##  [8,] -0.16432573 -0.16568601
##  [9,] -0.18110031 -0.18259945
## [10,] -0.20034915 -0.20200763
## [11,] -0.22252245 -0.22436448
## [12,] -0.24815572 -0.25020994
## [13,] -0.27787935 -0.28017962
## [14,] -0.31242211 -0.31500833
## [15,] -0.35260078 -0.35551960
## [16,] -0.39928184 -0.40258707
## [17,] -0.45329235 -0.45704468
## [18,] -0.51524502 -0.51951019
## [19,] -0.58523209 -0.59007662
## [20,] -0.66234790 -0.66783078
## [21,] -0.74405061 -0.75020983
## [22,] -0.82551448 -0.83234804
## [23,] -0.89936615 -0.90681105
## [24,] -0.95640716 -0.96432424
## [25,] -0.98772983 -0.99590621
## [26,] -0.98772983 -0.99590621
## [27,] -0.95640716 -0.96432424
## [28,] -0.89936615 -0.90681105
## [29,] -0.82551448 -0.83234804
## [30,] -0.74405061 -0.75020983
## [31,] -0.66234790 -0.66783078
## [32,] -0.58523209 -0.59007662
## [33,] -0.51524502 -0.51951019
## [34,] -0.45329235 -0.45704468
## [35,] -0.39928184 -0.40258707
## [36,] -0.35260078 -0.35551960
## [37,] -0.31242211 -0.31500833
## [38,] -0.27787935 -0.28017962
## [39,] -0.24815572 -0.25020994
## [40,] -0.22252245 -0.22436448
## [41,] -0.20034915 -0.20200763
## [42,] -0.18110031 -0.18259945
## [43,] -0.16432573 -0.16568601
## [44,] -0.14964899 -0.15088778
## [45,] -0.13675606 -0.13788811
## [46,] -0.12538502 -0.12642295
## [47,] -0.11531717 -0.11627176
## [48,] -0.10636947 -0.10724999
## [49,] -0.09838830 -0.09920276
## [50,] -0.09124435 -0.09199967
contour(x, y, f)
contour(x,y,f,nlevels=45,add=T)

fa <- (f-t(f))/2
contour(x,y,fa,nlevels=15)

  • image() to produce a color-coded plot whose colors depend on the z value (a.k.a. heatmap)
image(x,y,fa)

  • persp() to produce a three-dimensional plot known as a heatmap, and is sometimes used to plot temperature in weather forecasts. Alternatively, persp() can be used to . The arguments theta and phi control the angles at which the plot is persp() viewed.
persp(x,y,fa)

persp(x,y,fa,theta=30)

persp(x,y,fa,theta=30,phi=20)

persp(x,y,fa,theta=30,phi=70)

persp(x,y,fa,theta=30,phi=40)

1.3 Indexing data

Examining a subset of a dataset A

A <- matrix(1:16,4,4)
A
##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14
## [3,]    3    7   11   15
## [4,]    4    8   12   16
A[2,3]
## [1] 10
A[c(1,3),c(2,4)]
##      [,1] [,2]
## [1,]    5   13
## [2,]    7   15
A[1:3,2:4]
##      [,1] [,2] [,3]
## [1,]    5    9   13
## [2,]    6   10   14
## [3,]    7   11   15
A[1,]
## [1]  1  5  9 13
A[1:2,]
##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14
A[,1:2]
##      [,1] [,2]
## [1,]    1    5
## [2,]    2    6
## [3,]    3    7
## [4,]    4    8
A[-c(1,3),]
##      [,1] [,2] [,3] [,4]
## [1,]    2    6   10   14
## [2,]    4    8   12   16

dimensions

dim(A)
## [1] 4 4

1.4 Loading data

library(ISLR)
Auto
##      mpg cylinders displacement horsepower weight acceleration year origin
## 1   18.0         8        307.0        130   3504         12.0   70      1
## 2   15.0         8        350.0        165   3693         11.5   70      1
## 3   18.0         8        318.0        150   3436         11.0   70      1
## 4   16.0         8        304.0        150   3433         12.0   70      1
## 5   17.0         8        302.0        140   3449         10.5   70      1
## 6   15.0         8        429.0        198   4341         10.0   70      1
## 7   14.0         8        454.0        220   4354          9.0   70      1
## 8   14.0         8        440.0        215   4312          8.5   70      1
## 9   14.0         8        455.0        225   4425         10.0   70      1
## 10  15.0         8        390.0        190   3850          8.5   70      1
## 11  15.0         8        383.0        170   3563         10.0   70      1
## 12  14.0         8        340.0        160   3609          8.0   70      1
## 13  15.0         8        400.0        150   3761          9.5   70      1
## 14  14.0         8        455.0        225   3086         10.0   70      1
## 15  24.0         4        113.0         95   2372         15.0   70      3
## 16  22.0         6        198.0         95   2833         15.5   70      1
## 17  18.0         6        199.0         97   2774         15.5   70      1
## 18  21.0         6        200.0         85   2587         16.0   70      1
## 19  27.0         4         97.0         88   2130         14.5   70      3
## 20  26.0         4         97.0         46   1835         20.5   70      2
## 21  25.0         4        110.0         87   2672         17.5   70      2
## 22  24.0         4        107.0         90   2430         14.5   70      2
## 23  25.0         4        104.0         95   2375         17.5   70      2
## 24  26.0         4        121.0        113   2234         12.5   70      2
## 25  21.0         6        199.0         90   2648         15.0   70      1
## 26  10.0         8        360.0        215   4615         14.0   70      1
## 27  10.0         8        307.0        200   4376         15.0   70      1
## 28  11.0         8        318.0        210   4382         13.5   70      1
## 29   9.0         8        304.0        193   4732         18.5   70      1
## 30  27.0         4         97.0         88   2130         14.5   71      3
## 31  28.0         4        140.0         90   2264         15.5   71      1
## 32  25.0         4        113.0         95   2228         14.0   71      3
## 34  19.0         6        232.0        100   2634         13.0   71      1
## 35  16.0         6        225.0        105   3439         15.5   71      1
## 36  17.0         6        250.0        100   3329         15.5   71      1
## 37  19.0         6        250.0         88   3302         15.5   71      1
## 38  18.0         6        232.0        100   3288         15.5   71      1
## 39  14.0         8        350.0        165   4209         12.0   71      1
## 40  14.0         8        400.0        175   4464         11.5   71      1
## 41  14.0         8        351.0        153   4154         13.5   71      1
## 42  14.0         8        318.0        150   4096         13.0   71      1
## 43  12.0         8        383.0        180   4955         11.5   71      1
## 44  13.0         8        400.0        170   4746         12.0   71      1
## 45  13.0         8        400.0        175   5140         12.0   71      1
## 46  18.0         6        258.0        110   2962         13.5   71      1
## 47  22.0         4        140.0         72   2408         19.0   71      1
## 48  19.0         6        250.0        100   3282         15.0   71      1
## 49  18.0         6        250.0         88   3139         14.5   71      1
## 50  23.0         4        122.0         86   2220         14.0   71      1
## 51  28.0         4        116.0         90   2123         14.0   71      2
## 52  30.0         4         79.0         70   2074         19.5   71      2
## 53  30.0         4         88.0         76   2065         14.5   71      2
## 54  31.0         4         71.0         65   1773         19.0   71      3
## 55  35.0         4         72.0         69   1613         18.0   71      3
## 56  27.0         4         97.0         60   1834         19.0   71      2
## 57  26.0         4         91.0         70   1955         20.5   71      1
## 58  24.0         4        113.0         95   2278         15.5   72      3
## 59  25.0         4         97.5         80   2126         17.0   72      1
## 60  23.0         4         97.0         54   2254         23.5   72      2
## 61  20.0         4        140.0         90   2408         19.5   72      1
## 62  21.0         4        122.0         86   2226         16.5   72      1
## 63  13.0         8        350.0        165   4274         12.0   72      1
## 64  14.0         8        400.0        175   4385         12.0   72      1
## 65  15.0         8        318.0        150   4135         13.5   72      1
## 66  14.0         8        351.0        153   4129         13.0   72      1
## 67  17.0         8        304.0        150   3672         11.5   72      1
## 68  11.0         8        429.0        208   4633         11.0   72      1
## 69  13.0         8        350.0        155   4502         13.5   72      1
## 70  12.0         8        350.0        160   4456         13.5   72      1
## 71  13.0         8        400.0        190   4422         12.5   72      1
## 72  19.0         3         70.0         97   2330         13.5   72      3
## 73  15.0         8        304.0        150   3892         12.5   72      1
## 74  13.0         8        307.0        130   4098         14.0   72      1
## 75  13.0         8        302.0        140   4294         16.0   72      1
## 76  14.0         8        318.0        150   4077         14.0   72      1
## 77  18.0         4        121.0        112   2933         14.5   72      2
## 78  22.0         4        121.0         76   2511         18.0   72      2
## 79  21.0         4        120.0         87   2979         19.5   72      2
## 80  26.0         4         96.0         69   2189         18.0   72      2
## 81  22.0         4        122.0         86   2395         16.0   72      1
## 82  28.0         4         97.0         92   2288         17.0   72      3
## 83  23.0         4        120.0         97   2506         14.5   72      3
## 84  28.0         4         98.0         80   2164         15.0   72      1
## 85  27.0         4         97.0         88   2100         16.5   72      3
## 86  13.0         8        350.0        175   4100         13.0   73      1
## 87  14.0         8        304.0        150   3672         11.5   73      1
## 88  13.0         8        350.0        145   3988         13.0   73      1
## 89  14.0         8        302.0        137   4042         14.5   73      1
## 90  15.0         8        318.0        150   3777         12.5   73      1
## 91  12.0         8        429.0        198   4952         11.5   73      1
## 92  13.0         8        400.0        150   4464         12.0   73      1
## 93  13.0         8        351.0        158   4363         13.0   73      1
## 94  14.0         8        318.0        150   4237         14.5   73      1
## 95  13.0         8        440.0        215   4735         11.0   73      1
## 96  12.0         8        455.0        225   4951         11.0   73      1
## 97  13.0         8        360.0        175   3821         11.0   73      1
## 98  18.0         6        225.0        105   3121         16.5   73      1
## 99  16.0         6        250.0        100   3278         18.0   73      1
## 100 18.0         6        232.0        100   2945         16.0   73      1
## 101 18.0         6        250.0         88   3021         16.5   73      1
## 102 23.0         6        198.0         95   2904         16.0   73      1
## 103 26.0         4         97.0         46   1950         21.0   73      2
## 104 11.0         8        400.0        150   4997         14.0   73      1
## 105 12.0         8        400.0        167   4906         12.5   73      1
## 106 13.0         8        360.0        170   4654         13.0   73      1
## 107 12.0         8        350.0        180   4499         12.5   73      1
## 108 18.0         6        232.0        100   2789         15.0   73      1
## 109 20.0         4         97.0         88   2279         19.0   73      3
## 110 21.0         4        140.0         72   2401         19.5   73      1
## 111 22.0         4        108.0         94   2379         16.5   73      3
## 112 18.0         3         70.0         90   2124         13.5   73      3
## 113 19.0         4        122.0         85   2310         18.5   73      1
## 114 21.0         6        155.0        107   2472         14.0   73      1
## 115 26.0         4         98.0         90   2265         15.5   73      2
## 116 15.0         8        350.0        145   4082         13.0   73      1
## 117 16.0         8        400.0        230   4278          9.5   73      1
## 118 29.0         4         68.0         49   1867         19.5   73      2
## 119 24.0         4        116.0         75   2158         15.5   73      2
## 120 20.0         4        114.0         91   2582         14.0   73      2
## 121 19.0         4        121.0        112   2868         15.5   73      2
## 122 15.0         8        318.0        150   3399         11.0   73      1
## 123 24.0         4        121.0        110   2660         14.0   73      2
## 124 20.0         6        156.0        122   2807         13.5   73      3
## 125 11.0         8        350.0        180   3664         11.0   73      1
## 126 20.0         6        198.0         95   3102         16.5   74      1
## 128 19.0         6        232.0        100   2901         16.0   74      1
## 129 15.0         6        250.0        100   3336         17.0   74      1
## 130 31.0         4         79.0         67   1950         19.0   74      3
## 131 26.0         4        122.0         80   2451         16.5   74      1
## 132 32.0         4         71.0         65   1836         21.0   74      3
## 133 25.0         4        140.0         75   2542         17.0   74      1
## 134 16.0         6        250.0        100   3781         17.0   74      1
## 135 16.0         6        258.0        110   3632         18.0   74      1
## 136 18.0         6        225.0        105   3613         16.5   74      1
## 137 16.0         8        302.0        140   4141         14.0   74      1
## 138 13.0         8        350.0        150   4699         14.5   74      1
## 139 14.0         8        318.0        150   4457         13.5   74      1
## 140 14.0         8        302.0        140   4638         16.0   74      1
## 141 14.0         8        304.0        150   4257         15.5   74      1
## 142 29.0         4         98.0         83   2219         16.5   74      2
## 143 26.0         4         79.0         67   1963         15.5   74      2
## 144 26.0         4         97.0         78   2300         14.5   74      2
## 145 31.0         4         76.0         52   1649         16.5   74      3
## 146 32.0         4         83.0         61   2003         19.0   74      3
## 147 28.0         4         90.0         75   2125         14.5   74      1
## 148 24.0         4         90.0         75   2108         15.5   74      2
## 149 26.0         4        116.0         75   2246         14.0   74      2
## 150 24.0         4        120.0         97   2489         15.0   74      3
## 151 26.0         4        108.0         93   2391         15.5   74      3
## 152 31.0         4         79.0         67   2000         16.0   74      2
## 153 19.0         6        225.0         95   3264         16.0   75      1
## 154 18.0         6        250.0        105   3459         16.0   75      1
## 155 15.0         6        250.0         72   3432         21.0   75      1
## 156 15.0         6        250.0         72   3158         19.5   75      1
## 157 16.0         8        400.0        170   4668         11.5   75      1
## 158 15.0         8        350.0        145   4440         14.0   75      1
## 159 16.0         8        318.0        150   4498         14.5   75      1
## 160 14.0         8        351.0        148   4657         13.5   75      1
## 161 17.0         6        231.0        110   3907         21.0   75      1
## 162 16.0         6        250.0        105   3897         18.5   75      1
## 163 15.0         6        258.0        110   3730         19.0   75      1
## 164 18.0         6        225.0         95   3785         19.0   75      1
## 165 21.0         6        231.0        110   3039         15.0   75      1
## 166 20.0         8        262.0        110   3221         13.5   75      1
## 167 13.0         8        302.0        129   3169         12.0   75      1
## 168 29.0         4         97.0         75   2171         16.0   75      3
## 169 23.0         4        140.0         83   2639         17.0   75      1
## 170 20.0         6        232.0        100   2914         16.0   75      1
## 171 23.0         4        140.0         78   2592         18.5   75      1
## 172 24.0         4        134.0         96   2702         13.5   75      3
## 173 25.0         4         90.0         71   2223         16.5   75      2
## 174 24.0         4        119.0         97   2545         17.0   75      3
## 175 18.0         6        171.0         97   2984         14.5   75      1
## 176 29.0         4         90.0         70   1937         14.0   75      2
## 177 19.0         6        232.0         90   3211         17.0   75      1
## 178 23.0         4        115.0         95   2694         15.0   75      2
## 179 23.0         4        120.0         88   2957         17.0   75      2
## 180 22.0         4        121.0         98   2945         14.5   75      2
## 181 25.0         4        121.0        115   2671         13.5   75      2
## 182 33.0         4         91.0         53   1795         17.5   75      3
## 183 28.0         4        107.0         86   2464         15.5   76      2
## 184 25.0         4        116.0         81   2220         16.9   76      2
## 185 25.0         4        140.0         92   2572         14.9   76      1
## 186 26.0         4         98.0         79   2255         17.7   76      1
## 187 27.0         4        101.0         83   2202         15.3   76      2
## 188 17.5         8        305.0        140   4215         13.0   76      1
## 189 16.0         8        318.0        150   4190         13.0   76      1
## 190 15.5         8        304.0        120   3962         13.9   76      1
## 191 14.5         8        351.0        152   4215         12.8   76      1
## 192 22.0         6        225.0        100   3233         15.4   76      1
## 193 22.0         6        250.0        105   3353         14.5   76      1
## 194 24.0         6        200.0         81   3012         17.6   76      1
## 195 22.5         6        232.0         90   3085         17.6   76      1
## 196 29.0         4         85.0         52   2035         22.2   76      1
## 197 24.5         4         98.0         60   2164         22.1   76      1
## 198 29.0         4         90.0         70   1937         14.2   76      2
## 199 33.0         4         91.0         53   1795         17.4   76      3
## 200 20.0         6        225.0        100   3651         17.7   76      1
## 201 18.0         6        250.0         78   3574         21.0   76      1
## 202 18.5         6        250.0        110   3645         16.2   76      1
## 203 17.5         6        258.0         95   3193         17.8   76      1
## 204 29.5         4         97.0         71   1825         12.2   76      2
## 205 32.0         4         85.0         70   1990         17.0   76      3
## 206 28.0         4         97.0         75   2155         16.4   76      3
## 207 26.5         4        140.0         72   2565         13.6   76      1
## 208 20.0         4        130.0        102   3150         15.7   76      2
## 209 13.0         8        318.0        150   3940         13.2   76      1
## 210 19.0         4        120.0         88   3270         21.9   76      2
## 211 19.0         6        156.0        108   2930         15.5   76      3
## 212 16.5         6        168.0        120   3820         16.7   76      2
## 213 16.5         8        350.0        180   4380         12.1   76      1
## 214 13.0         8        350.0        145   4055         12.0   76      1
## 215 13.0         8        302.0        130   3870         15.0   76      1
## 216 13.0         8        318.0        150   3755         14.0   76      1
## 217 31.5         4         98.0         68   2045         18.5   77      3
## 218 30.0         4        111.0         80   2155         14.8   77      1
## 219 36.0         4         79.0         58   1825         18.6   77      2
## 220 25.5         4        122.0         96   2300         15.5   77      1
## 221 33.5         4         85.0         70   1945         16.8   77      3
## 222 17.5         8        305.0        145   3880         12.5   77      1
## 223 17.0         8        260.0        110   4060         19.0   77      1
## 224 15.5         8        318.0        145   4140         13.7   77      1
## 225 15.0         8        302.0        130   4295         14.9   77      1
## 226 17.5         6        250.0        110   3520         16.4   77      1
## 227 20.5         6        231.0        105   3425         16.9   77      1
## 228 19.0         6        225.0        100   3630         17.7   77      1
## 229 18.5         6        250.0         98   3525         19.0   77      1
## 230 16.0         8        400.0        180   4220         11.1   77      1
## 231 15.5         8        350.0        170   4165         11.4   77      1
## 232 15.5         8        400.0        190   4325         12.2   77      1
## 233 16.0         8        351.0        149   4335         14.5   77      1
## 234 29.0         4         97.0         78   1940         14.5   77      2
## 235 24.5         4        151.0         88   2740         16.0   77      1
## 236 26.0         4         97.0         75   2265         18.2   77      3
## 237 25.5         4        140.0         89   2755         15.8   77      1
## 238 30.5         4         98.0         63   2051         17.0   77      1
## 239 33.5         4         98.0         83   2075         15.9   77      1
## 240 30.0         4         97.0         67   1985         16.4   77      3
## 241 30.5         4         97.0         78   2190         14.1   77      2
## 242 22.0         6        146.0         97   2815         14.5   77      3
## 243 21.5         4        121.0        110   2600         12.8   77      2
## 244 21.5         3         80.0        110   2720         13.5   77      3
## 245 43.1         4         90.0         48   1985         21.5   78      2
## 246 36.1         4         98.0         66   1800         14.4   78      1
## 247 32.8         4         78.0         52   1985         19.4   78      3
## 248 39.4         4         85.0         70   2070         18.6   78      3
## 249 36.1         4         91.0         60   1800         16.4   78      3
## 250 19.9         8        260.0        110   3365         15.5   78      1
## 251 19.4         8        318.0        140   3735         13.2   78      1
## 252 20.2         8        302.0        139   3570         12.8   78      1
## 253 19.2         6        231.0        105   3535         19.2   78      1
## 254 20.5         6        200.0         95   3155         18.2   78      1
## 255 20.2         6        200.0         85   2965         15.8   78      1
## 256 25.1         4        140.0         88   2720         15.4   78      1
## 257 20.5         6        225.0        100   3430         17.2   78      1
## 258 19.4         6        232.0         90   3210         17.2   78      1
## 259 20.6         6        231.0        105   3380         15.8   78      1
## 260 20.8         6        200.0         85   3070         16.7   78      1
## 261 18.6         6        225.0        110   3620         18.7   78      1
## 262 18.1         6        258.0        120   3410         15.1   78      1
## 263 19.2         8        305.0        145   3425         13.2   78      1
## 264 17.7         6        231.0        165   3445         13.4   78      1
## 265 18.1         8        302.0        139   3205         11.2   78      1
## 266 17.5         8        318.0        140   4080         13.7   78      1
## 267 30.0         4         98.0         68   2155         16.5   78      1
## 268 27.5         4        134.0         95   2560         14.2   78      3
## 269 27.2         4        119.0         97   2300         14.7   78      3
## 270 30.9         4        105.0         75   2230         14.5   78      1
## 271 21.1         4        134.0         95   2515         14.8   78      3
## 272 23.2         4        156.0        105   2745         16.7   78      1
## 273 23.8         4        151.0         85   2855         17.6   78      1
## 274 23.9         4        119.0         97   2405         14.9   78      3
## 275 20.3         5        131.0        103   2830         15.9   78      2
## 276 17.0         6        163.0        125   3140         13.6   78      2
## 277 21.6         4        121.0        115   2795         15.7   78      2
## 278 16.2         6        163.0        133   3410         15.8   78      2
## 279 31.5         4         89.0         71   1990         14.9   78      2
## 280 29.5         4         98.0         68   2135         16.6   78      3
## 281 21.5         6        231.0        115   3245         15.4   79      1
## 282 19.8         6        200.0         85   2990         18.2   79      1
## 283 22.3         4        140.0         88   2890         17.3   79      1
## 284 20.2         6        232.0         90   3265         18.2   79      1
## 285 20.6         6        225.0        110   3360         16.6   79      1
## 286 17.0         8        305.0        130   3840         15.4   79      1
## 287 17.6         8        302.0        129   3725         13.4   79      1
## 288 16.5         8        351.0        138   3955         13.2   79      1
## 289 18.2         8        318.0        135   3830         15.2   79      1
## 290 16.9         8        350.0        155   4360         14.9   79      1
## 291 15.5         8        351.0        142   4054         14.3   79      1
## 292 19.2         8        267.0        125   3605         15.0   79      1
## 293 18.5         8        360.0        150   3940         13.0   79      1
## 294 31.9         4         89.0         71   1925         14.0   79      2
## 295 34.1         4         86.0         65   1975         15.2   79      3
## 296 35.7         4         98.0         80   1915         14.4   79      1
## 297 27.4         4        121.0         80   2670         15.0   79      1
## 298 25.4         5        183.0         77   3530         20.1   79      2
## 299 23.0         8        350.0        125   3900         17.4   79      1
## 300 27.2         4        141.0         71   3190         24.8   79      2
## 301 23.9         8        260.0         90   3420         22.2   79      1
## 302 34.2         4        105.0         70   2200         13.2   79      1
## 303 34.5         4        105.0         70   2150         14.9   79      1
## 304 31.8         4         85.0         65   2020         19.2   79      3
## 305 37.3         4         91.0         69   2130         14.7   79      2
## 306 28.4         4        151.0         90   2670         16.0   79      1
## 307 28.8         6        173.0        115   2595         11.3   79      1
## 308 26.8         6        173.0        115   2700         12.9   79      1
## 309 33.5         4        151.0         90   2556         13.2   79      1
## 310 41.5         4         98.0         76   2144         14.7   80      2
## 311 38.1         4         89.0         60   1968         18.8   80      3
## 312 32.1         4         98.0         70   2120         15.5   80      1
## 313 37.2         4         86.0         65   2019         16.4   80      3
## 314 28.0         4        151.0         90   2678         16.5   80      1
## 315 26.4         4        140.0         88   2870         18.1   80      1
## 316 24.3         4        151.0         90   3003         20.1   80      1
## 317 19.1         6        225.0         90   3381         18.7   80      1
## 318 34.3         4         97.0         78   2188         15.8   80      2
## 319 29.8         4        134.0         90   2711         15.5   80      3
## 320 31.3         4        120.0         75   2542         17.5   80      3
## 321 37.0         4        119.0         92   2434         15.0   80      3
## 322 32.2         4        108.0         75   2265         15.2   80      3
## 323 46.6         4         86.0         65   2110         17.9   80      3
## 324 27.9         4        156.0        105   2800         14.4   80      1
## 325 40.8         4         85.0         65   2110         19.2   80      3
## 326 44.3         4         90.0         48   2085         21.7   80      2
## 327 43.4         4         90.0         48   2335         23.7   80      2
## 328 36.4         5        121.0         67   2950         19.9   80      2
## 329 30.0         4        146.0         67   3250         21.8   80      2
## 330 44.6         4         91.0         67   1850         13.8   80      3
## 332 33.8         4         97.0         67   2145         18.0   80      3
## 333 29.8         4         89.0         62   1845         15.3   80      2
## 334 32.7         6        168.0        132   2910         11.4   80      3
## 335 23.7         3         70.0        100   2420         12.5   80      3
## 336 35.0         4        122.0         88   2500         15.1   80      2
## 338 32.4         4        107.0         72   2290         17.0   80      3
## 339 27.2         4        135.0         84   2490         15.7   81      1
## 340 26.6         4        151.0         84   2635         16.4   81      1
## 341 25.8         4        156.0         92   2620         14.4   81      1
## 342 23.5         6        173.0        110   2725         12.6   81      1
## 343 30.0         4        135.0         84   2385         12.9   81      1
## 344 39.1         4         79.0         58   1755         16.9   81      3
## 345 39.0         4         86.0         64   1875         16.4   81      1
## 346 35.1         4         81.0         60   1760         16.1   81      3
## 347 32.3         4         97.0         67   2065         17.8   81      3
## 348 37.0         4         85.0         65   1975         19.4   81      3
## 349 37.7         4         89.0         62   2050         17.3   81      3
## 350 34.1         4         91.0         68   1985         16.0   81      3
## 351 34.7         4        105.0         63   2215         14.9   81      1
## 352 34.4         4         98.0         65   2045         16.2   81      1
## 353 29.9         4         98.0         65   2380         20.7   81      1
## 354 33.0         4        105.0         74   2190         14.2   81      2
## 356 33.7         4        107.0         75   2210         14.4   81      3
## 357 32.4         4        108.0         75   2350         16.8   81      3
## 358 32.9         4        119.0        100   2615         14.8   81      3
## 359 31.6         4        120.0         74   2635         18.3   81      3
## 360 28.1         4        141.0         80   3230         20.4   81      2
## 361 30.7         6        145.0         76   3160         19.6   81      2
## 362 25.4         6        168.0        116   2900         12.6   81      3
## 363 24.2         6        146.0        120   2930         13.8   81      3
## 364 22.4         6        231.0        110   3415         15.8   81      1
## 365 26.6         8        350.0        105   3725         19.0   81      1
## 366 20.2         6        200.0         88   3060         17.1   81      1
## 367 17.6         6        225.0         85   3465         16.6   81      1
## 368 28.0         4        112.0         88   2605         19.6   82      1
## 369 27.0         4        112.0         88   2640         18.6   82      1
## 370 34.0         4        112.0         88   2395         18.0   82      1
## 371 31.0         4        112.0         85   2575         16.2   82      1
## 372 29.0         4        135.0         84   2525         16.0   82      1
## 373 27.0         4        151.0         90   2735         18.0   82      1
## 374 24.0         4        140.0         92   2865         16.4   82      1
## 375 36.0         4        105.0         74   1980         15.3   82      2
## 376 37.0         4         91.0         68   2025         18.2   82      3
## 377 31.0         4         91.0         68   1970         17.6   82      3
## 378 38.0         4        105.0         63   2125         14.7   82      1
## 379 36.0         4         98.0         70   2125         17.3   82      1
## 380 36.0         4        120.0         88   2160         14.5   82      3
## 381 36.0         4        107.0         75   2205         14.5   82      3
## 382 34.0         4        108.0         70   2245         16.9   82      3
## 383 38.0         4         91.0         67   1965         15.0   82      3
## 384 32.0         4         91.0         67   1965         15.7   82      3
## 385 38.0         4         91.0         67   1995         16.2   82      3
## 386 25.0         6        181.0        110   2945         16.4   82      1
## 387 38.0         6        262.0         85   3015         17.0   82      1
## 388 26.0         4        156.0         92   2585         14.5   82      1
## 389 22.0         6        232.0        112   2835         14.7   82      1
## 390 32.0         4        144.0         96   2665         13.9   82      3
## 391 36.0         4        135.0         84   2370         13.0   82      1
## 392 27.0         4        151.0         90   2950         17.3   82      1
## 393 27.0         4        140.0         86   2790         15.6   82      1
## 394 44.0         4         97.0         52   2130         24.6   82      2
## 395 32.0         4        135.0         84   2295         11.6   82      1
## 396 28.0         4        120.0         79   2625         18.6   82      1
## 397 31.0         4        119.0         82   2720         19.4   82      1
##                                     name
## 1              chevrolet chevelle malibu
## 2                      buick skylark 320
## 3                     plymouth satellite
## 4                          amc rebel sst
## 5                            ford torino
## 6                       ford galaxie 500
## 7                       chevrolet impala
## 8                      plymouth fury iii
## 9                       pontiac catalina
## 10                    amc ambassador dpl
## 11                   dodge challenger se
## 12                    plymouth 'cuda 340
## 13                 chevrolet monte carlo
## 14               buick estate wagon (sw)
## 15                 toyota corona mark ii
## 16                       plymouth duster
## 17                            amc hornet
## 18                         ford maverick
## 19                          datsun pl510
## 20          volkswagen 1131 deluxe sedan
## 21                           peugeot 504
## 22                           audi 100 ls
## 23                              saab 99e
## 24                              bmw 2002
## 25                           amc gremlin
## 26                             ford f250
## 27                             chevy c20
## 28                            dodge d200
## 29                              hi 1200d
## 30                          datsun pl510
## 31                   chevrolet vega 2300
## 32                         toyota corona
## 34                           amc gremlin
## 35             plymouth satellite custom
## 36             chevrolet chevelle malibu
## 37                       ford torino 500
## 38                           amc matador
## 39                      chevrolet impala
## 40             pontiac catalina brougham
## 41                      ford galaxie 500
## 42                     plymouth fury iii
## 43                     dodge monaco (sw)
## 44              ford country squire (sw)
## 45                   pontiac safari (sw)
## 46            amc hornet sportabout (sw)
## 47                   chevrolet vega (sw)
## 48                      pontiac firebird
## 49                          ford mustang
## 50                    mercury capri 2000
## 51                             opel 1900
## 52                           peugeot 304
## 53                             fiat 124b
## 54                   toyota corolla 1200
## 55                           datsun 1200
## 56                  volkswagen model 111
## 57                      plymouth cricket
## 58                 toyota corona hardtop
## 59                    dodge colt hardtop
## 60                     volkswagen type 3
## 61                        chevrolet vega
## 62                   ford pinto runabout
## 63                      chevrolet impala
## 64                      pontiac catalina
## 65                     plymouth fury iii
## 66                      ford galaxie 500
## 67                    amc ambassador sst
## 68                       mercury marquis
## 69                  buick lesabre custom
## 70            oldsmobile delta 88 royale
## 71                chrysler newport royal
## 72                       mazda rx2 coupe
## 73                      amc matador (sw)
## 74      chevrolet chevelle concours (sw)
## 75                 ford gran torino (sw)
## 76        plymouth satellite custom (sw)
## 77                       volvo 145e (sw)
## 78                   volkswagen 411 (sw)
## 79                      peugeot 504 (sw)
## 80                       renault 12 (sw)
## 81                       ford pinto (sw)
## 82                       datsun 510 (sw)
## 83           toyouta corona mark ii (sw)
## 84                       dodge colt (sw)
## 85              toyota corolla 1600 (sw)
## 86                     buick century 350
## 87                           amc matador
## 88                      chevrolet malibu
## 89                      ford gran torino
## 90                  dodge coronet custom
## 91              mercury marquis brougham
## 92             chevrolet caprice classic
## 93                              ford ltd
## 94              plymouth fury gran sedan
## 95          chrysler new yorker brougham
## 96              buick electra 225 custom
## 97               amc ambassador brougham
## 98                      plymouth valiant
## 99                 chevrolet nova custom
## 100                           amc hornet
## 101                        ford maverick
## 102                      plymouth duster
## 103              volkswagen super beetle
## 104                     chevrolet impala
## 105                         ford country
## 106               plymouth custom suburb
## 107             oldsmobile vista cruiser
## 108                          amc gremlin
## 109                        toyota carina
## 110                       chevrolet vega
## 111                           datsun 610
## 112                            maxda rx3
## 113                           ford pinto
## 114                     mercury capri v6
## 115                 fiat 124 sport coupe
## 116              chevrolet monte carlo s
## 117                   pontiac grand prix
## 118                             fiat 128
## 119                           opel manta
## 120                           audi 100ls
## 121                          volvo 144ea
## 122                    dodge dart custom
## 123                            saab 99le
## 124                       toyota mark ii
## 125                     oldsmobile omega
## 126                      plymouth duster
## 128                           amc hornet
## 129                       chevrolet nova
## 130                          datsun b210
## 131                           ford pinto
## 132                  toyota corolla 1200
## 133                       chevrolet vega
## 134    chevrolet chevelle malibu classic
## 135                          amc matador
## 136           plymouth satellite sebring
## 137                     ford gran torino
## 138             buick century luxus (sw)
## 139            dodge coronet custom (sw)
## 140                ford gran torino (sw)
## 141                     amc matador (sw)
## 142                             audi fox
## 143                    volkswagen dasher
## 144                           opel manta
## 145                        toyota corona
## 146                           datsun 710
## 147                           dodge colt
## 148                             fiat 128
## 149                          fiat 124 tc
## 150                          honda civic
## 151                               subaru
## 152                            fiat x1.9
## 153              plymouth valiant custom
## 154                       chevrolet nova
## 155                      mercury monarch
## 156                        ford maverick
## 157                     pontiac catalina
## 158                    chevrolet bel air
## 159                  plymouth grand fury
## 160                             ford ltd
## 161                        buick century
## 162            chevroelt chevelle malibu
## 163                          amc matador
## 164                        plymouth fury
## 165                        buick skyhawk
## 166                  chevrolet monza 2+2
## 167                      ford mustang ii
## 168                       toyota corolla
## 169                           ford pinto
## 170                          amc gremlin
## 171                        pontiac astro
## 172                        toyota corona
## 173                    volkswagen dasher
## 174                           datsun 710
## 175                           ford pinto
## 176                    volkswagen rabbit
## 177                            amc pacer
## 178                           audi 100ls
## 179                          peugeot 504
## 180                          volvo 244dl
## 181                            saab 99le
## 182                     honda civic cvcc
## 183                             fiat 131
## 184                            opel 1900
## 185                             capri ii
## 186                           dodge colt
## 187                         renault 12tl
## 188    chevrolet chevelle malibu classic
## 189               dodge coronet brougham
## 190                          amc matador
## 191                     ford gran torino
## 192                     plymouth valiant
## 193                       chevrolet nova
## 194                        ford maverick
## 195                           amc hornet
## 196                   chevrolet chevette
## 197                      chevrolet woody
## 198                            vw rabbit
## 199                          honda civic
## 200                       dodge aspen se
## 201                    ford granada ghia
## 202                   pontiac ventura sj
## 203                        amc pacer d/l
## 204                    volkswagen rabbit
## 205                         datsun b-210
## 206                       toyota corolla
## 207                           ford pinto
## 208                            volvo 245
## 209           plymouth volare premier v8
## 210                          peugeot 504
## 211                       toyota mark ii
## 212                   mercedes-benz 280s
## 213                     cadillac seville
## 214                            chevy c10
## 215                            ford f108
## 216                           dodge d100
## 217                    honda accord cvcc
## 218              buick opel isuzu deluxe
## 219                        renault 5 gtl
## 220                    plymouth arrow gs
## 221                datsun f-10 hatchback
## 222            chevrolet caprice classic
## 223           oldsmobile cutlass supreme
## 224                dodge monaco brougham
## 225              mercury cougar brougham
## 226                   chevrolet concours
## 227                        buick skylark
## 228               plymouth volare custom
## 229                         ford granada
## 230                pontiac grand prix lj
## 231         chevrolet monte carlo landau
## 232                     chrysler cordoba
## 233                     ford thunderbird
## 234             volkswagen rabbit custom
## 235                pontiac sunbird coupe
## 236              toyota corolla liftback
## 237                  ford mustang ii 2+2
## 238                   chevrolet chevette
## 239                       dodge colt m/m
## 240                            subaru dl
## 241                    volkswagen dasher
## 242                           datsun 810
## 243                             bmw 320i
## 244                           mazda rx-4
## 245      volkswagen rabbit custom diesel
## 246                          ford fiesta
## 247                     mazda glc deluxe
## 248                       datsun b210 gx
## 249                     honda civic cvcc
## 250    oldsmobile cutlass salon brougham
## 251                       dodge diplomat
## 252                 mercury monarch ghia
## 253                   pontiac phoenix lj
## 254                     chevrolet malibu
## 255                 ford fairmont (auto)
## 256                  ford fairmont (man)
## 257                      plymouth volare
## 258                          amc concord
## 259                buick century special
## 260                       mercury zephyr
## 261                          dodge aspen
## 262                      amc concord d/l
## 263         chevrolet monte carlo landau
## 264      buick regal sport coupe (turbo)
## 265                          ford futura
## 266                      dodge magnum xe
## 267                   chevrolet chevette
## 268                        toyota corona
## 269                           datsun 510
## 270                           dodge omni
## 271            toyota celica gt liftback
## 272                     plymouth sapporo
## 273               oldsmobile starfire sx
## 274                        datsun 200-sx
## 275                            audi 5000
## 276                          volvo 264gl
## 277                           saab 99gle
## 278                        peugeot 604sl
## 279                  volkswagen scirocco
## 280                      honda accord lx
## 281                    pontiac lemans v6
## 282                     mercury zephyr 6
## 283                      ford fairmont 4
## 284                     amc concord dl 6
## 285                        dodge aspen 6
## 286            chevrolet caprice classic
## 287                      ford ltd landau
## 288                mercury grand marquis
## 289                      dodge st. regis
## 290              buick estate wagon (sw)
## 291             ford country squire (sw)
## 292        chevrolet malibu classic (sw)
## 293 chrysler lebaron town @ country (sw)
## 294                     vw rabbit custom
## 295                     maxda glc deluxe
## 296          dodge colt hatchback custom
## 297                        amc spirit dl
## 298                   mercedes benz 300d
## 299                    cadillac eldorado
## 300                          peugeot 504
## 301    oldsmobile cutlass salon brougham
## 302                     plymouth horizon
## 303                 plymouth horizon tc3
## 304                           datsun 210
## 305                   fiat strada custom
## 306                buick skylark limited
## 307                   chevrolet citation
## 308            oldsmobile omega brougham
## 309                      pontiac phoenix
## 310                            vw rabbit
## 311                toyota corolla tercel
## 312                   chevrolet chevette
## 313                           datsun 310
## 314                   chevrolet citation
## 315                        ford fairmont
## 316                          amc concord
## 317                          dodge aspen
## 318                            audi 4000
## 319               toyota corona liftback
## 320                            mazda 626
## 321                 datsun 510 hatchback
## 322                       toyota corolla
## 323                            mazda glc
## 324                           dodge colt
## 325                           datsun 210
## 326                 vw rabbit c (diesel)
## 327                   vw dasher (diesel)
## 328                  audi 5000s (diesel)
## 329                   mercedes-benz 240d
## 330                  honda civic 1500 gl
## 332                            subaru dl
## 333                     vokswagen rabbit
## 334                        datsun 280-zx
## 335                        mazda rx-7 gs
## 336                    triumph tr7 coupe
## 338                         honda accord
## 339                     plymouth reliant
## 340                        buick skylark
## 341               dodge aries wagon (sw)
## 342                   chevrolet citation
## 343                     plymouth reliant
## 344                       toyota starlet
## 345                       plymouth champ
## 346                     honda civic 1300
## 347                               subaru
## 348                       datsun 210 mpg
## 349                        toyota tercel
## 350                          mazda glc 4
## 351                   plymouth horizon 4
## 352                       ford escort 4w
## 353                       ford escort 2h
## 354                     volkswagen jetta
## 356                        honda prelude
## 357                       toyota corolla
## 358                         datsun 200sx
## 359                            mazda 626
## 360            peugeot 505s turbo diesel
## 361                         volvo diesel
## 362                      toyota cressida
## 363                    datsun 810 maxima
## 364                        buick century
## 365                oldsmobile cutlass ls
## 366                      ford granada gl
## 367               chrysler lebaron salon
## 368                   chevrolet cavalier
## 369             chevrolet cavalier wagon
## 370            chevrolet cavalier 2-door
## 371           pontiac j2000 se hatchback
## 372                       dodge aries se
## 373                      pontiac phoenix
## 374                 ford fairmont futura
## 375                  volkswagen rabbit l
## 376                   mazda glc custom l
## 377                     mazda glc custom
## 378               plymouth horizon miser
## 379                       mercury lynx l
## 380                     nissan stanza xe
## 381                         honda accord
## 382                       toyota corolla
## 383                          honda civic
## 384                   honda civic (auto)
## 385                        datsun 310 gx
## 386                buick century limited
## 387    oldsmobile cutlass ciera (diesel)
## 388           chrysler lebaron medallion
## 389                       ford granada l
## 390                     toyota celica gt
## 391                    dodge charger 2.2
## 392                     chevrolet camaro
## 393                      ford mustang gl
## 394                            vw pickup
## 395                        dodge rampage
## 396                          ford ranger
## 397                           chevy s-10
write.table(Auto, file = "Auto.txt")
read.table(file = "Auto.txt")
##      mpg cylinders displacement horsepower weight acceleration year origin
## 1   18.0         8        307.0        130   3504         12.0   70      1
## 2   15.0         8        350.0        165   3693         11.5   70      1
## 3   18.0         8        318.0        150   3436         11.0   70      1
## 4   16.0         8        304.0        150   3433         12.0   70      1
## 5   17.0         8        302.0        140   3449         10.5   70      1
## 6   15.0         8        429.0        198   4341         10.0   70      1
## 7   14.0         8        454.0        220   4354          9.0   70      1
## 8   14.0         8        440.0        215   4312          8.5   70      1
## 9   14.0         8        455.0        225   4425         10.0   70      1
## 10  15.0         8        390.0        190   3850          8.5   70      1
## 11  15.0         8        383.0        170   3563         10.0   70      1
## 12  14.0         8        340.0        160   3609          8.0   70      1
## 13  15.0         8        400.0        150   3761          9.5   70      1
## 14  14.0         8        455.0        225   3086         10.0   70      1
## 15  24.0         4        113.0         95   2372         15.0   70      3
## 16  22.0         6        198.0         95   2833         15.5   70      1
## 17  18.0         6        199.0         97   2774         15.5   70      1
## 18  21.0         6        200.0         85   2587         16.0   70      1
## 19  27.0         4         97.0         88   2130         14.5   70      3
## 20  26.0         4         97.0         46   1835         20.5   70      2
## 21  25.0         4        110.0         87   2672         17.5   70      2
## 22  24.0         4        107.0         90   2430         14.5   70      2
## 23  25.0         4        104.0         95   2375         17.5   70      2
## 24  26.0         4        121.0        113   2234         12.5   70      2
## 25  21.0         6        199.0         90   2648         15.0   70      1
## 26  10.0         8        360.0        215   4615         14.0   70      1
## 27  10.0         8        307.0        200   4376         15.0   70      1
## 28  11.0         8        318.0        210   4382         13.5   70      1
## 29   9.0         8        304.0        193   4732         18.5   70      1
## 30  27.0         4         97.0         88   2130         14.5   71      3
## 31  28.0         4        140.0         90   2264         15.5   71      1
## 32  25.0         4        113.0         95   2228         14.0   71      3
## 34  19.0         6        232.0        100   2634         13.0   71      1
## 35  16.0         6        225.0        105   3439         15.5   71      1
## 36  17.0         6        250.0        100   3329         15.5   71      1
## 37  19.0         6        250.0         88   3302         15.5   71      1
## 38  18.0         6        232.0        100   3288         15.5   71      1
## 39  14.0         8        350.0        165   4209         12.0   71      1
## 40  14.0         8        400.0        175   4464         11.5   71      1
## 41  14.0         8        351.0        153   4154         13.5   71      1
## 42  14.0         8        318.0        150   4096         13.0   71      1
## 43  12.0         8        383.0        180   4955         11.5   71      1
## 44  13.0         8        400.0        170   4746         12.0   71      1
## 45  13.0         8        400.0        175   5140         12.0   71      1
## 46  18.0         6        258.0        110   2962         13.5   71      1
## 47  22.0         4        140.0         72   2408         19.0   71      1
## 48  19.0         6        250.0        100   3282         15.0   71      1
## 49  18.0         6        250.0         88   3139         14.5   71      1
## 50  23.0         4        122.0         86   2220         14.0   71      1
## 51  28.0         4        116.0         90   2123         14.0   71      2
## 52  30.0         4         79.0         70   2074         19.5   71      2
## 53  30.0         4         88.0         76   2065         14.5   71      2
## 54  31.0         4         71.0         65   1773         19.0   71      3
## 55  35.0         4         72.0         69   1613         18.0   71      3
## 56  27.0         4         97.0         60   1834         19.0   71      2
## 57  26.0         4         91.0         70   1955         20.5   71      1
## 58  24.0         4        113.0         95   2278         15.5   72      3
## 59  25.0         4         97.5         80   2126         17.0   72      1
## 60  23.0         4         97.0         54   2254         23.5   72      2
## 61  20.0         4        140.0         90   2408         19.5   72      1
## 62  21.0         4        122.0         86   2226         16.5   72      1
## 63  13.0         8        350.0        165   4274         12.0   72      1
## 64  14.0         8        400.0        175   4385         12.0   72      1
## 65  15.0         8        318.0        150   4135         13.5   72      1
## 66  14.0         8        351.0        153   4129         13.0   72      1
## 67  17.0         8        304.0        150   3672         11.5   72      1
## 68  11.0         8        429.0        208   4633         11.0   72      1
## 69  13.0         8        350.0        155   4502         13.5   72      1
## 70  12.0         8        350.0        160   4456         13.5   72      1
## 71  13.0         8        400.0        190   4422         12.5   72      1
## 72  19.0         3         70.0         97   2330         13.5   72      3
## 73  15.0         8        304.0        150   3892         12.5   72      1
## 74  13.0         8        307.0        130   4098         14.0   72      1
## 75  13.0         8        302.0        140   4294         16.0   72      1
## 76  14.0         8        318.0        150   4077         14.0   72      1
## 77  18.0         4        121.0        112   2933         14.5   72      2
## 78  22.0         4        121.0         76   2511         18.0   72      2
## 79  21.0         4        120.0         87   2979         19.5   72      2
## 80  26.0         4         96.0         69   2189         18.0   72      2
## 81  22.0         4        122.0         86   2395         16.0   72      1
## 82  28.0         4         97.0         92   2288         17.0   72      3
## 83  23.0         4        120.0         97   2506         14.5   72      3
## 84  28.0         4         98.0         80   2164         15.0   72      1
## 85  27.0         4         97.0         88   2100         16.5   72      3
## 86  13.0         8        350.0        175   4100         13.0   73      1
## 87  14.0         8        304.0        150   3672         11.5   73      1
## 88  13.0         8        350.0        145   3988         13.0   73      1
## 89  14.0         8        302.0        137   4042         14.5   73      1
## 90  15.0         8        318.0        150   3777         12.5   73      1
## 91  12.0         8        429.0        198   4952         11.5   73      1
## 92  13.0         8        400.0        150   4464         12.0   73      1
## 93  13.0         8        351.0        158   4363         13.0   73      1
## 94  14.0         8        318.0        150   4237         14.5   73      1
## 95  13.0         8        440.0        215   4735         11.0   73      1
## 96  12.0         8        455.0        225   4951         11.0   73      1
## 97  13.0         8        360.0        175   3821         11.0   73      1
## 98  18.0         6        225.0        105   3121         16.5   73      1
## 99  16.0         6        250.0        100   3278         18.0   73      1
## 100 18.0         6        232.0        100   2945         16.0   73      1
## 101 18.0         6        250.0         88   3021         16.5   73      1
## 102 23.0         6        198.0         95   2904         16.0   73      1
## 103 26.0         4         97.0         46   1950         21.0   73      2
## 104 11.0         8        400.0        150   4997         14.0   73      1
## 105 12.0         8        400.0        167   4906         12.5   73      1
## 106 13.0         8        360.0        170   4654         13.0   73      1
## 107 12.0         8        350.0        180   4499         12.5   73      1
## 108 18.0         6        232.0        100   2789         15.0   73      1
## 109 20.0         4         97.0         88   2279         19.0   73      3
## 110 21.0         4        140.0         72   2401         19.5   73      1
## 111 22.0         4        108.0         94   2379         16.5   73      3
## 112 18.0         3         70.0         90   2124         13.5   73      3
## 113 19.0         4        122.0         85   2310         18.5   73      1
## 114 21.0         6        155.0        107   2472         14.0   73      1
## 115 26.0         4         98.0         90   2265         15.5   73      2
## 116 15.0         8        350.0        145   4082         13.0   73      1
## 117 16.0         8        400.0        230   4278          9.5   73      1
## 118 29.0         4         68.0         49   1867         19.5   73      2
## 119 24.0         4        116.0         75   2158         15.5   73      2
## 120 20.0         4        114.0         91   2582         14.0   73      2
## 121 19.0         4        121.0        112   2868         15.5   73      2
## 122 15.0         8        318.0        150   3399         11.0   73      1
## 123 24.0         4        121.0        110   2660         14.0   73      2
## 124 20.0         6        156.0        122   2807         13.5   73      3
## 125 11.0         8        350.0        180   3664         11.0   73      1
## 126 20.0         6        198.0         95   3102         16.5   74      1
## 128 19.0         6        232.0        100   2901         16.0   74      1
## 129 15.0         6        250.0        100   3336         17.0   74      1
## 130 31.0         4         79.0         67   1950         19.0   74      3
## 131 26.0         4        122.0         80   2451         16.5   74      1
## 132 32.0         4         71.0         65   1836         21.0   74      3
## 133 25.0         4        140.0         75   2542         17.0   74      1
## 134 16.0         6        250.0        100   3781         17.0   74      1
## 135 16.0         6        258.0        110   3632         18.0   74      1
## 136 18.0         6        225.0        105   3613         16.5   74      1
## 137 16.0         8        302.0        140   4141         14.0   74      1
## 138 13.0         8        350.0        150   4699         14.5   74      1
## 139 14.0         8        318.0        150   4457         13.5   74      1
## 140 14.0         8        302.0        140   4638         16.0   74      1
## 141 14.0         8        304.0        150   4257         15.5   74      1
## 142 29.0         4         98.0         83   2219         16.5   74      2
## 143 26.0         4         79.0         67   1963         15.5   74      2
## 144 26.0         4         97.0         78   2300         14.5   74      2
## 145 31.0         4         76.0         52   1649         16.5   74      3
## 146 32.0         4         83.0         61   2003         19.0   74      3
## 147 28.0         4         90.0         75   2125         14.5   74      1
## 148 24.0         4         90.0         75   2108         15.5   74      2
## 149 26.0         4        116.0         75   2246         14.0   74      2
## 150 24.0         4        120.0         97   2489         15.0   74      3
## 151 26.0         4        108.0         93   2391         15.5   74      3
## 152 31.0         4         79.0         67   2000         16.0   74      2
## 153 19.0         6        225.0         95   3264         16.0   75      1
## 154 18.0         6        250.0        105   3459         16.0   75      1
## 155 15.0         6        250.0         72   3432         21.0   75      1
## 156 15.0         6        250.0         72   3158         19.5   75      1
## 157 16.0         8        400.0        170   4668         11.5   75      1
## 158 15.0         8        350.0        145   4440         14.0   75      1
## 159 16.0         8        318.0        150   4498         14.5   75      1
## 160 14.0         8        351.0        148   4657         13.5   75      1
## 161 17.0         6        231.0        110   3907         21.0   75      1
## 162 16.0         6        250.0        105   3897         18.5   75      1
## 163 15.0         6        258.0        110   3730         19.0   75      1
## 164 18.0         6        225.0         95   3785         19.0   75      1
## 165 21.0         6        231.0        110   3039         15.0   75      1
## 166 20.0         8        262.0        110   3221         13.5   75      1
## 167 13.0         8        302.0        129   3169         12.0   75      1
## 168 29.0         4         97.0         75   2171         16.0   75      3
## 169 23.0         4        140.0         83   2639         17.0   75      1
## 170 20.0         6        232.0        100   2914         16.0   75      1
## 171 23.0         4        140.0         78   2592         18.5   75      1
## 172 24.0         4        134.0         96   2702         13.5   75      3
## 173 25.0         4         90.0         71   2223         16.5   75      2
## 174 24.0         4        119.0         97   2545         17.0   75      3
## 175 18.0         6        171.0         97   2984         14.5   75      1
## 176 29.0         4         90.0         70   1937         14.0   75      2
## 177 19.0         6        232.0         90   3211         17.0   75      1
## 178 23.0         4        115.0         95   2694         15.0   75      2
## 179 23.0         4        120.0         88   2957         17.0   75      2
## 180 22.0         4        121.0         98   2945         14.5   75      2
## 181 25.0         4        121.0        115   2671         13.5   75      2
## 182 33.0         4         91.0         53   1795         17.5   75      3
## 183 28.0         4        107.0         86   2464         15.5   76      2
## 184 25.0         4        116.0         81   2220         16.9   76      2
## 185 25.0         4        140.0         92   2572         14.9   76      1
## 186 26.0         4         98.0         79   2255         17.7   76      1
## 187 27.0         4        101.0         83   2202         15.3   76      2
## 188 17.5         8        305.0        140   4215         13.0   76      1
## 189 16.0         8        318.0        150   4190         13.0   76      1
## 190 15.5         8        304.0        120   3962         13.9   76      1
## 191 14.5         8        351.0        152   4215         12.8   76      1
## 192 22.0         6        225.0        100   3233         15.4   76      1
## 193 22.0         6        250.0        105   3353         14.5   76      1
## 194 24.0         6        200.0         81   3012         17.6   76      1
## 195 22.5         6        232.0         90   3085         17.6   76      1
## 196 29.0         4         85.0         52   2035         22.2   76      1
## 197 24.5         4         98.0         60   2164         22.1   76      1
## 198 29.0         4         90.0         70   1937         14.2   76      2
## 199 33.0         4         91.0         53   1795         17.4   76      3
## 200 20.0         6        225.0        100   3651         17.7   76      1
## 201 18.0         6        250.0         78   3574         21.0   76      1
## 202 18.5         6        250.0        110   3645         16.2   76      1
## 203 17.5         6        258.0         95   3193         17.8   76      1
## 204 29.5         4         97.0         71   1825         12.2   76      2
## 205 32.0         4         85.0         70   1990         17.0   76      3
## 206 28.0         4         97.0         75   2155         16.4   76      3
## 207 26.5         4        140.0         72   2565         13.6   76      1
## 208 20.0         4        130.0        102   3150         15.7   76      2
## 209 13.0         8        318.0        150   3940         13.2   76      1
## 210 19.0         4        120.0         88   3270         21.9   76      2
## 211 19.0         6        156.0        108   2930         15.5   76      3
## 212 16.5         6        168.0        120   3820         16.7   76      2
## 213 16.5         8        350.0        180   4380         12.1   76      1
## 214 13.0         8        350.0        145   4055         12.0   76      1
## 215 13.0         8        302.0        130   3870         15.0   76      1
## 216 13.0         8        318.0        150   3755         14.0   76      1
## 217 31.5         4         98.0         68   2045         18.5   77      3
## 218 30.0         4        111.0         80   2155         14.8   77      1
## 219 36.0         4         79.0         58   1825         18.6   77      2
## 220 25.5         4        122.0         96   2300         15.5   77      1
## 221 33.5         4         85.0         70   1945         16.8   77      3
## 222 17.5         8        305.0        145   3880         12.5   77      1
## 223 17.0         8        260.0        110   4060         19.0   77      1
## 224 15.5         8        318.0        145   4140         13.7   77      1
## 225 15.0         8        302.0        130   4295         14.9   77      1
## 226 17.5         6        250.0        110   3520         16.4   77      1
## 227 20.5         6        231.0        105   3425         16.9   77      1
## 228 19.0         6        225.0        100   3630         17.7   77      1
## 229 18.5         6        250.0         98   3525         19.0   77      1
## 230 16.0         8        400.0        180   4220         11.1   77      1
## 231 15.5         8        350.0        170   4165         11.4   77      1
## 232 15.5         8        400.0        190   4325         12.2   77      1
## 233 16.0         8        351.0        149   4335         14.5   77      1
## 234 29.0         4         97.0         78   1940         14.5   77      2
## 235 24.5         4        151.0         88   2740         16.0   77      1
## 236 26.0         4         97.0         75   2265         18.2   77      3
## 237 25.5         4        140.0         89   2755         15.8   77      1
## 238 30.5         4         98.0         63   2051         17.0   77      1
## 239 33.5         4         98.0         83   2075         15.9   77      1
## 240 30.0         4         97.0         67   1985         16.4   77      3
## 241 30.5         4         97.0         78   2190         14.1   77      2
## 242 22.0         6        146.0         97   2815         14.5   77      3
## 243 21.5         4        121.0        110   2600         12.8   77      2
## 244 21.5         3         80.0        110   2720         13.5   77      3
## 245 43.1         4         90.0         48   1985         21.5   78      2
## 246 36.1         4         98.0         66   1800         14.4   78      1
## 247 32.8         4         78.0         52   1985         19.4   78      3
## 248 39.4         4         85.0         70   2070         18.6   78      3
## 249 36.1         4         91.0         60   1800         16.4   78      3
## 250 19.9         8        260.0        110   3365         15.5   78      1
## 251 19.4         8        318.0        140   3735         13.2   78      1
## 252 20.2         8        302.0        139   3570         12.8   78      1
## 253 19.2         6        231.0        105   3535         19.2   78      1
## 254 20.5         6        200.0         95   3155         18.2   78      1
## 255 20.2         6        200.0         85   2965         15.8   78      1
## 256 25.1         4        140.0         88   2720         15.4   78      1
## 257 20.5         6        225.0        100   3430         17.2   78      1
## 258 19.4         6        232.0         90   3210         17.2   78      1
## 259 20.6         6        231.0        105   3380         15.8   78      1
## 260 20.8         6        200.0         85   3070         16.7   78      1
## 261 18.6         6        225.0        110   3620         18.7   78      1
## 262 18.1         6        258.0        120   3410         15.1   78      1
## 263 19.2         8        305.0        145   3425         13.2   78      1
## 264 17.7         6        231.0        165   3445         13.4   78      1
## 265 18.1         8        302.0        139   3205         11.2   78      1
## 266 17.5         8        318.0        140   4080         13.7   78      1
## 267 30.0         4         98.0         68   2155         16.5   78      1
## 268 27.5         4        134.0         95   2560         14.2   78      3
## 269 27.2         4        119.0         97   2300         14.7   78      3
## 270 30.9         4        105.0         75   2230         14.5   78      1
## 271 21.1         4        134.0         95   2515         14.8   78      3
## 272 23.2         4        156.0        105   2745         16.7   78      1
## 273 23.8         4        151.0         85   2855         17.6   78      1
## 274 23.9         4        119.0         97   2405         14.9   78      3
## 275 20.3         5        131.0        103   2830         15.9   78      2
## 276 17.0         6        163.0        125   3140         13.6   78      2
## 277 21.6         4        121.0        115   2795         15.7   78      2
## 278 16.2         6        163.0        133   3410         15.8   78      2
## 279 31.5         4         89.0         71   1990         14.9   78      2
## 280 29.5         4         98.0         68   2135         16.6   78      3
## 281 21.5         6        231.0        115   3245         15.4   79      1
## 282 19.8         6        200.0         85   2990         18.2   79      1
## 283 22.3         4        140.0         88   2890         17.3   79      1
## 284 20.2         6        232.0         90   3265         18.2   79      1
## 285 20.6         6        225.0        110   3360         16.6   79      1
## 286 17.0         8        305.0        130   3840         15.4   79      1
## 287 17.6         8        302.0        129   3725         13.4   79      1
## 288 16.5         8        351.0        138   3955         13.2   79      1
## 289 18.2         8        318.0        135   3830         15.2   79      1
## 290 16.9         8        350.0        155   4360         14.9   79      1
## 291 15.5         8        351.0        142   4054         14.3   79      1
## 292 19.2         8        267.0        125   3605         15.0   79      1
## 293 18.5         8        360.0        150   3940         13.0   79      1
## 294 31.9         4         89.0         71   1925         14.0   79      2
## 295 34.1         4         86.0         65   1975         15.2   79      3
## 296 35.7         4         98.0         80   1915         14.4   79      1
## 297 27.4         4        121.0         80   2670         15.0   79      1
## 298 25.4         5        183.0         77   3530         20.1   79      2
## 299 23.0         8        350.0        125   3900         17.4   79      1
## 300 27.2         4        141.0         71   3190         24.8   79      2
## 301 23.9         8        260.0         90   3420         22.2   79      1
## 302 34.2         4        105.0         70   2200         13.2   79      1
## 303 34.5         4        105.0         70   2150         14.9   79      1
## 304 31.8         4         85.0         65   2020         19.2   79      3
## 305 37.3         4         91.0         69   2130         14.7   79      2
## 306 28.4         4        151.0         90   2670         16.0   79      1
## 307 28.8         6        173.0        115   2595         11.3   79      1
## 308 26.8         6        173.0        115   2700         12.9   79      1
## 309 33.5         4        151.0         90   2556         13.2   79      1
## 310 41.5         4         98.0         76   2144         14.7   80      2
## 311 38.1         4         89.0         60   1968         18.8   80      3
## 312 32.1         4         98.0         70   2120         15.5   80      1
## 313 37.2         4         86.0         65   2019         16.4   80      3
## 314 28.0         4        151.0         90   2678         16.5   80      1
## 315 26.4         4        140.0         88   2870         18.1   80      1
## 316 24.3         4        151.0         90   3003         20.1   80      1
## 317 19.1         6        225.0         90   3381         18.7   80      1
## 318 34.3         4         97.0         78   2188         15.8   80      2
## 319 29.8         4        134.0         90   2711         15.5   80      3
## 320 31.3         4        120.0         75   2542         17.5   80      3
## 321 37.0         4        119.0         92   2434         15.0   80      3
## 322 32.2         4        108.0         75   2265         15.2   80      3
## 323 46.6         4         86.0         65   2110         17.9   80      3
## 324 27.9         4        156.0        105   2800         14.4   80      1
## 325 40.8         4         85.0         65   2110         19.2   80      3
## 326 44.3         4         90.0         48   2085         21.7   80      2
## 327 43.4         4         90.0         48   2335         23.7   80      2
## 328 36.4         5        121.0         67   2950         19.9   80      2
## 329 30.0         4        146.0         67   3250         21.8   80      2
## 330 44.6         4         91.0         67   1850         13.8   80      3
## 332 33.8         4         97.0         67   2145         18.0   80      3
## 333 29.8         4         89.0         62   1845         15.3   80      2
## 334 32.7         6        168.0        132   2910         11.4   80      3
## 335 23.7         3         70.0        100   2420         12.5   80      3
## 336 35.0         4        122.0         88   2500         15.1   80      2
## 338 32.4         4        107.0         72   2290         17.0   80      3
## 339 27.2         4        135.0         84   2490         15.7   81      1
## 340 26.6         4        151.0         84   2635         16.4   81      1
## 341 25.8         4        156.0         92   2620         14.4   81      1
## 342 23.5         6        173.0        110   2725         12.6   81      1
## 343 30.0         4        135.0         84   2385         12.9   81      1
## 344 39.1         4         79.0         58   1755         16.9   81      3
## 345 39.0         4         86.0         64   1875         16.4   81      1
## 346 35.1         4         81.0         60   1760         16.1   81      3
## 347 32.3         4         97.0         67   2065         17.8   81      3
## 348 37.0         4         85.0         65   1975         19.4   81      3
## 349 37.7         4         89.0         62   2050         17.3   81      3
## 350 34.1         4         91.0         68   1985         16.0   81      3
## 351 34.7         4        105.0         63   2215         14.9   81      1
## 352 34.4         4         98.0         65   2045         16.2   81      1
## 353 29.9         4         98.0         65   2380         20.7   81      1
## 354 33.0         4        105.0         74   2190         14.2   81      2
## 356 33.7         4        107.0         75   2210         14.4   81      3
## 357 32.4         4        108.0         75   2350         16.8   81      3
## 358 32.9         4        119.0        100   2615         14.8   81      3
## 359 31.6         4        120.0         74   2635         18.3   81      3
## 360 28.1         4        141.0         80   3230         20.4   81      2
## 361 30.7         6        145.0         76   3160         19.6   81      2
## 362 25.4         6        168.0        116   2900         12.6   81      3
## 363 24.2         6        146.0        120   2930         13.8   81      3
## 364 22.4         6        231.0        110   3415         15.8   81      1
## 365 26.6         8        350.0        105   3725         19.0   81      1
## 366 20.2         6        200.0         88   3060         17.1   81      1
## 367 17.6         6        225.0         85   3465         16.6   81      1
## 368 28.0         4        112.0         88   2605         19.6   82      1
## 369 27.0         4        112.0         88   2640         18.6   82      1
## 370 34.0         4        112.0         88   2395         18.0   82      1
## 371 31.0         4        112.0         85   2575         16.2   82      1
## 372 29.0         4        135.0         84   2525         16.0   82      1
## 373 27.0         4        151.0         90   2735         18.0   82      1
## 374 24.0         4        140.0         92   2865         16.4   82      1
## 375 36.0         4        105.0         74   1980         15.3   82      2
## 376 37.0         4         91.0         68   2025         18.2   82      3
## 377 31.0         4         91.0         68   1970         17.6   82      3
## 378 38.0         4        105.0         63   2125         14.7   82      1
## 379 36.0         4         98.0         70   2125         17.3   82      1
## 380 36.0         4        120.0         88   2160         14.5   82      3
## 381 36.0         4        107.0         75   2205         14.5   82      3
## 382 34.0         4        108.0         70   2245         16.9   82      3
## 383 38.0         4         91.0         67   1965         15.0   82      3
## 384 32.0         4         91.0         67   1965         15.7   82      3
## 385 38.0         4         91.0         67   1995         16.2   82      3
## 386 25.0         6        181.0        110   2945         16.4   82      1
## 387 38.0         6        262.0         85   3015         17.0   82      1
## 388 26.0         4        156.0         92   2585         14.5   82      1
## 389 22.0         6        232.0        112   2835         14.7   82      1
## 390 32.0         4        144.0         96   2665         13.9   82      3
## 391 36.0         4        135.0         84   2370         13.0   82      1
## 392 27.0         4        151.0         90   2950         17.3   82      1
## 393 27.0         4        140.0         86   2790         15.6   82      1
## 394 44.0         4         97.0         52   2130         24.6   82      2
## 395 32.0         4        135.0         84   2295         11.6   82      1
## 396 28.0         4        120.0         79   2625         18.6   82      1
## 397 31.0         4        119.0         82   2720         19.4   82      1
##                                     name
## 1              chevrolet chevelle malibu
## 2                      buick skylark 320
## 3                     plymouth satellite
## 4                          amc rebel sst
## 5                            ford torino
## 6                       ford galaxie 500
## 7                       chevrolet impala
## 8                      plymouth fury iii
## 9                       pontiac catalina
## 10                    amc ambassador dpl
## 11                   dodge challenger se
## 12                    plymouth 'cuda 340
## 13                 chevrolet monte carlo
## 14               buick estate wagon (sw)
## 15                 toyota corona mark ii
## 16                       plymouth duster
## 17                            amc hornet
## 18                         ford maverick
## 19                          datsun pl510
## 20          volkswagen 1131 deluxe sedan
## 21                           peugeot 504
## 22                           audi 100 ls
## 23                              saab 99e
## 24                              bmw 2002
## 25                           amc gremlin
## 26                             ford f250
## 27                             chevy c20
## 28                            dodge d200
## 29                              hi 1200d
## 30                          datsun pl510
## 31                   chevrolet vega 2300
## 32                         toyota corona
## 34                           amc gremlin
## 35             plymouth satellite custom
## 36             chevrolet chevelle malibu
## 37                       ford torino 500
## 38                           amc matador
## 39                      chevrolet impala
## 40             pontiac catalina brougham
## 41                      ford galaxie 500
## 42                     plymouth fury iii
## 43                     dodge monaco (sw)
## 44              ford country squire (sw)
## 45                   pontiac safari (sw)
## 46            amc hornet sportabout (sw)
## 47                   chevrolet vega (sw)
## 48                      pontiac firebird
## 49                          ford mustang
## 50                    mercury capri 2000
## 51                             opel 1900
## 52                           peugeot 304
## 53                             fiat 124b
## 54                   toyota corolla 1200
## 55                           datsun 1200
## 56                  volkswagen model 111
## 57                      plymouth cricket
## 58                 toyota corona hardtop
## 59                    dodge colt hardtop
## 60                     volkswagen type 3
## 61                        chevrolet vega
## 62                   ford pinto runabout
## 63                      chevrolet impala
## 64                      pontiac catalina
## 65                     plymouth fury iii
## 66                      ford galaxie 500
## 67                    amc ambassador sst
## 68                       mercury marquis
## 69                  buick lesabre custom
## 70            oldsmobile delta 88 royale
## 71                chrysler newport royal
## 72                       mazda rx2 coupe
## 73                      amc matador (sw)
## 74      chevrolet chevelle concours (sw)
## 75                 ford gran torino (sw)
## 76        plymouth satellite custom (sw)
## 77                       volvo 145e (sw)
## 78                   volkswagen 411 (sw)
## 79                      peugeot 504 (sw)
## 80                       renault 12 (sw)
## 81                       ford pinto (sw)
## 82                       datsun 510 (sw)
## 83           toyouta corona mark ii (sw)
## 84                       dodge colt (sw)
## 85              toyota corolla 1600 (sw)
## 86                     buick century 350
## 87                           amc matador
## 88                      chevrolet malibu
## 89                      ford gran torino
## 90                  dodge coronet custom
## 91              mercury marquis brougham
## 92             chevrolet caprice classic
## 93                              ford ltd
## 94              plymouth fury gran sedan
## 95          chrysler new yorker brougham
## 96              buick electra 225 custom
## 97               amc ambassador brougham
## 98                      plymouth valiant
## 99                 chevrolet nova custom
## 100                           amc hornet
## 101                        ford maverick
## 102                      plymouth duster
## 103              volkswagen super beetle
## 104                     chevrolet impala
## 105                         ford country
## 106               plymouth custom suburb
## 107             oldsmobile vista cruiser
## 108                          amc gremlin
## 109                        toyota carina
## 110                       chevrolet vega
## 111                           datsun 610
## 112                            maxda rx3
## 113                           ford pinto
## 114                     mercury capri v6
## 115                 fiat 124 sport coupe
## 116              chevrolet monte carlo s
## 117                   pontiac grand prix
## 118                             fiat 128
## 119                           opel manta
## 120                           audi 100ls
## 121                          volvo 144ea
## 122                    dodge dart custom
## 123                            saab 99le
## 124                       toyota mark ii
## 125                     oldsmobile omega
## 126                      plymouth duster
## 128                           amc hornet
## 129                       chevrolet nova
## 130                          datsun b210
## 131                           ford pinto
## 132                  toyota corolla 1200
## 133                       chevrolet vega
## 134    chevrolet chevelle malibu classic
## 135                          amc matador
## 136           plymouth satellite sebring
## 137                     ford gran torino
## 138             buick century luxus (sw)
## 139            dodge coronet custom (sw)
## 140                ford gran torino (sw)
## 141                     amc matador (sw)
## 142                             audi fox
## 143                    volkswagen dasher
## 144                           opel manta
## 145                        toyota corona
## 146                           datsun 710
## 147                           dodge colt
## 148                             fiat 128
## 149                          fiat 124 tc
## 150                          honda civic
## 151                               subaru
## 152                            fiat x1.9
## 153              plymouth valiant custom
## 154                       chevrolet nova
## 155                      mercury monarch
## 156                        ford maverick
## 157                     pontiac catalina
## 158                    chevrolet bel air
## 159                  plymouth grand fury
## 160                             ford ltd
## 161                        buick century
## 162            chevroelt chevelle malibu
## 163                          amc matador
## 164                        plymouth fury
## 165                        buick skyhawk
## 166                  chevrolet monza 2+2
## 167                      ford mustang ii
## 168                       toyota corolla
## 169                           ford pinto
## 170                          amc gremlin
## 171                        pontiac astro
## 172                        toyota corona
## 173                    volkswagen dasher
## 174                           datsun 710
## 175                           ford pinto
## 176                    volkswagen rabbit
## 177                            amc pacer
## 178                           audi 100ls
## 179                          peugeot 504
## 180                          volvo 244dl
## 181                            saab 99le
## 182                     honda civic cvcc
## 183                             fiat 131
## 184                            opel 1900
## 185                             capri ii
## 186                           dodge colt
## 187                         renault 12tl
## 188    chevrolet chevelle malibu classic
## 189               dodge coronet brougham
## 190                          amc matador
## 191                     ford gran torino
## 192                     plymouth valiant
## 193                       chevrolet nova
## 194                        ford maverick
## 195                           amc hornet
## 196                   chevrolet chevette
## 197                      chevrolet woody
## 198                            vw rabbit
## 199                          honda civic
## 200                       dodge aspen se
## 201                    ford granada ghia
## 202                   pontiac ventura sj
## 203                        amc pacer d/l
## 204                    volkswagen rabbit
## 205                         datsun b-210
## 206                       toyota corolla
## 207                           ford pinto
## 208                            volvo 245
## 209           plymouth volare premier v8
## 210                          peugeot 504
## 211                       toyota mark ii
## 212                   mercedes-benz 280s
## 213                     cadillac seville
## 214                            chevy c10
## 215                            ford f108
## 216                           dodge d100
## 217                    honda accord cvcc
## 218              buick opel isuzu deluxe
## 219                        renault 5 gtl
## 220                    plymouth arrow gs
## 221                datsun f-10 hatchback
## 222            chevrolet caprice classic
## 223           oldsmobile cutlass supreme
## 224                dodge monaco brougham
## 225              mercury cougar brougham
## 226                   chevrolet concours
## 227                        buick skylark
## 228               plymouth volare custom
## 229                         ford granada
## 230                pontiac grand prix lj
## 231         chevrolet monte carlo landau
## 232                     chrysler cordoba
## 233                     ford thunderbird
## 234             volkswagen rabbit custom
## 235                pontiac sunbird coupe
## 236              toyota corolla liftback
## 237                  ford mustang ii 2+2
## 238                   chevrolet chevette
## 239                       dodge colt m/m
## 240                            subaru dl
## 241                    volkswagen dasher
## 242                           datsun 810
## 243                             bmw 320i
## 244                           mazda rx-4
## 245      volkswagen rabbit custom diesel
## 246                          ford fiesta
## 247                     mazda glc deluxe
## 248                       datsun b210 gx
## 249                     honda civic cvcc
## 250    oldsmobile cutlass salon brougham
## 251                       dodge diplomat
## 252                 mercury monarch ghia
## 253                   pontiac phoenix lj
## 254                     chevrolet malibu
## 255                 ford fairmont (auto)
## 256                  ford fairmont (man)
## 257                      plymouth volare
## 258                          amc concord
## 259                buick century special
## 260                       mercury zephyr
## 261                          dodge aspen
## 262                      amc concord d/l
## 263         chevrolet monte carlo landau
## 264      buick regal sport coupe (turbo)
## 265                          ford futura
## 266                      dodge magnum xe
## 267                   chevrolet chevette
## 268                        toyota corona
## 269                           datsun 510
## 270                           dodge omni
## 271            toyota celica gt liftback
## 272                     plymouth sapporo
## 273               oldsmobile starfire sx
## 274                        datsun 200-sx
## 275                            audi 5000
## 276                          volvo 264gl
## 277                           saab 99gle
## 278                        peugeot 604sl
## 279                  volkswagen scirocco
## 280                      honda accord lx
## 281                    pontiac lemans v6
## 282                     mercury zephyr 6
## 283                      ford fairmont 4
## 284                     amc concord dl 6
## 285                        dodge aspen 6
## 286            chevrolet caprice classic
## 287                      ford ltd landau
## 288                mercury grand marquis
## 289                      dodge st. regis
## 290              buick estate wagon (sw)
## 291             ford country squire (sw)
## 292        chevrolet malibu classic (sw)
## 293 chrysler lebaron town @ country (sw)
## 294                     vw rabbit custom
## 295                     maxda glc deluxe
## 296          dodge colt hatchback custom
## 297                        amc spirit dl
## 298                   mercedes benz 300d
## 299                    cadillac eldorado
## 300                          peugeot 504
## 301    oldsmobile cutlass salon brougham
## 302                     plymouth horizon
## 303                 plymouth horizon tc3
## 304                           datsun 210
## 305                   fiat strada custom
## 306                buick skylark limited
## 307                   chevrolet citation
## 308            oldsmobile omega brougham
## 309                      pontiac phoenix
## 310                            vw rabbit
## 311                toyota corolla tercel
## 312                   chevrolet chevette
## 313                           datsun 310
## 314                   chevrolet citation
## 315                        ford fairmont
## 316                          amc concord
## 317                          dodge aspen
## 318                            audi 4000
## 319               toyota corona liftback
## 320                            mazda 626
## 321                 datsun 510 hatchback
## 322                       toyota corolla
## 323                            mazda glc
## 324                           dodge colt
## 325                           datsun 210
## 326                 vw rabbit c (diesel)
## 327                   vw dasher (diesel)
## 328                  audi 5000s (diesel)
## 329                   mercedes-benz 240d
## 330                  honda civic 1500 gl
## 332                            subaru dl
## 333                     vokswagen rabbit
## 334                        datsun 280-zx
## 335                        mazda rx-7 gs
## 336                    triumph tr7 coupe
## 338                         honda accord
## 339                     plymouth reliant
## 340                        buick skylark
## 341               dodge aries wagon (sw)
## 342                   chevrolet citation
## 343                     plymouth reliant
## 344                       toyota starlet
## 345                       plymouth champ
## 346                     honda civic 1300
## 347                               subaru
## 348                       datsun 210 mpg
## 349                        toyota tercel
## 350                          mazda glc 4
## 351                   plymouth horizon 4
## 352                       ford escort 4w
## 353                       ford escort 2h
## 354                     volkswagen jetta
## 356                        honda prelude
## 357                       toyota corolla
## 358                         datsun 200sx
## 359                            mazda 626
## 360            peugeot 505s turbo diesel
## 361                         volvo diesel
## 362                      toyota cressida
## 363                    datsun 810 maxima
## 364                        buick century
## 365                oldsmobile cutlass ls
## 366                      ford granada gl
## 367               chrysler lebaron salon
## 368                   chevrolet cavalier
## 369             chevrolet cavalier wagon
## 370            chevrolet cavalier 2-door
## 371           pontiac j2000 se hatchback
## 372                       dodge aries se
## 373                      pontiac phoenix
## 374                 ford fairmont futura
## 375                  volkswagen rabbit l
## 376                   mazda glc custom l
## 377                     mazda glc custom
## 378               plymouth horizon miser
## 379                       mercury lynx l
## 380                     nissan stanza xe
## 381                         honda accord
## 382                       toyota corolla
## 383                          honda civic
## 384                   honda civic (auto)
## 385                        datsun 310 gx
## 386                buick century limited
## 387    oldsmobile cutlass ciera (diesel)
## 388           chrysler lebaron medallion
## 389                       ford granada l
## 390                     toyota celica gt
## 391                    dodge charger 2.2
## 392                     chevrolet camaro
## 393                      ford mustang gl
## 394                            vw pickup
## 395                        dodge rampage
## 396                          ford ranger
## 397                           chevy s-10
?read.csv

# fix(Auto)
View(Auto)
knitr::kable(Auto)
mpg cylinders displacement horsepower weight acceleration year origin name
1 18.0 8 307.0 130 3504 12.0 70 1 chevrolet chevelle malibu
2 15.0 8 350.0 165 3693 11.5 70 1 buick skylark 320
3 18.0 8 318.0 150 3436 11.0 70 1 plymouth satellite
4 16.0 8 304.0 150 3433 12.0 70 1 amc rebel sst
5 17.0 8 302.0 140 3449 10.5 70 1 ford torino
6 15.0 8 429.0 198 4341 10.0 70 1 ford galaxie 500
7 14.0 8 454.0 220 4354 9.0 70 1 chevrolet impala
8 14.0 8 440.0 215 4312 8.5 70 1 plymouth fury iii
9 14.0 8 455.0 225 4425 10.0 70 1 pontiac catalina
10 15.0 8 390.0 190 3850 8.5 70 1 amc ambassador dpl
11 15.0 8 383.0 170 3563 10.0 70 1 dodge challenger se
12 14.0 8 340.0 160 3609 8.0 70 1 plymouth ’cuda 340
13 15.0 8 400.0 150 3761 9.5 70 1 chevrolet monte carlo
14 14.0 8 455.0 225 3086 10.0 70 1 buick estate wagon (sw)
15 24.0 4 113.0 95 2372 15.0 70 3 toyota corona mark ii
16 22.0 6 198.0 95 2833 15.5 70 1 plymouth duster
17 18.0 6 199.0 97 2774 15.5 70 1 amc hornet
18 21.0 6 200.0 85 2587 16.0 70 1 ford maverick
19 27.0 4 97.0 88 2130 14.5 70 3 datsun pl510
20 26.0 4 97.0 46 1835 20.5 70 2 volkswagen 1131 deluxe sedan
21 25.0 4 110.0 87 2672 17.5 70 2 peugeot 504
22 24.0 4 107.0 90 2430 14.5 70 2 audi 100 ls
23 25.0 4 104.0 95 2375 17.5 70 2 saab 99e
24 26.0 4 121.0 113 2234 12.5 70 2 bmw 2002
25 21.0 6 199.0 90 2648 15.0 70 1 amc gremlin
26 10.0 8 360.0 215 4615 14.0 70 1 ford f250
27 10.0 8 307.0 200 4376 15.0 70 1 chevy c20
28 11.0 8 318.0 210 4382 13.5 70 1 dodge d200
29 9.0 8 304.0 193 4732 18.5 70 1 hi 1200d
30 27.0 4 97.0 88 2130 14.5 71 3 datsun pl510
31 28.0 4 140.0 90 2264 15.5 71 1 chevrolet vega 2300
32 25.0 4 113.0 95 2228 14.0 71 3 toyota corona
34 19.0 6 232.0 100 2634 13.0 71 1 amc gremlin
35 16.0 6 225.0 105 3439 15.5 71 1 plymouth satellite custom
36 17.0 6 250.0 100 3329 15.5 71 1 chevrolet chevelle malibu
37 19.0 6 250.0 88 3302 15.5 71 1 ford torino 500
38 18.0 6 232.0 100 3288 15.5 71 1 amc matador
39 14.0 8 350.0 165 4209 12.0 71 1 chevrolet impala
40 14.0 8 400.0 175 4464 11.5 71 1 pontiac catalina brougham
41 14.0 8 351.0 153 4154 13.5 71 1 ford galaxie 500
42 14.0 8 318.0 150 4096 13.0 71 1 plymouth fury iii
43 12.0 8 383.0 180 4955 11.5 71 1 dodge monaco (sw)
44 13.0 8 400.0 170 4746 12.0 71 1 ford country squire (sw)
45 13.0 8 400.0 175 5140 12.0 71 1 pontiac safari (sw)
46 18.0 6 258.0 110 2962 13.5 71 1 amc hornet sportabout (sw)
47 22.0 4 140.0 72 2408 19.0 71 1 chevrolet vega (sw)
48 19.0 6 250.0 100 3282 15.0 71 1 pontiac firebird
49 18.0 6 250.0 88 3139 14.5 71 1 ford mustang
50 23.0 4 122.0 86 2220 14.0 71 1 mercury capri 2000
51 28.0 4 116.0 90 2123 14.0 71 2 opel 1900
52 30.0 4 79.0 70 2074 19.5 71 2 peugeot 304
53 30.0 4 88.0 76 2065 14.5 71 2 fiat 124b
54 31.0 4 71.0 65 1773 19.0 71 3 toyota corolla 1200
55 35.0 4 72.0 69 1613 18.0 71 3 datsun 1200
56 27.0 4 97.0 60 1834 19.0 71 2 volkswagen model 111
57 26.0 4 91.0 70 1955 20.5 71 1 plymouth cricket
58 24.0 4 113.0 95 2278 15.5 72 3 toyota corona hardtop
59 25.0 4 97.5 80 2126 17.0 72 1 dodge colt hardtop
60 23.0 4 97.0 54 2254 23.5 72 2 volkswagen type 3
61 20.0 4 140.0 90 2408 19.5 72 1 chevrolet vega
62 21.0 4 122.0 86 2226 16.5 72 1 ford pinto runabout
63 13.0 8 350.0 165 4274 12.0 72 1 chevrolet impala
64 14.0 8 400.0 175 4385 12.0 72 1 pontiac catalina
65 15.0 8 318.0 150 4135 13.5 72 1 plymouth fury iii
66 14.0 8 351.0 153 4129 13.0 72 1 ford galaxie 500
67 17.0 8 304.0 150 3672 11.5 72 1 amc ambassador sst
68 11.0 8 429.0 208 4633 11.0 72 1 mercury marquis
69 13.0 8 350.0 155 4502 13.5 72 1 buick lesabre custom
70 12.0 8 350.0 160 4456 13.5 72 1 oldsmobile delta 88 royale
71 13.0 8 400.0 190 4422 12.5 72 1 chrysler newport royal
72 19.0 3 70.0 97 2330 13.5 72 3 mazda rx2 coupe
73 15.0 8 304.0 150 3892 12.5 72 1 amc matador (sw)
74 13.0 8 307.0 130 4098 14.0 72 1 chevrolet chevelle concours (sw)
75 13.0 8 302.0 140 4294 16.0 72 1 ford gran torino (sw)
76 14.0 8 318.0 150 4077 14.0 72 1 plymouth satellite custom (sw)
77 18.0 4 121.0 112 2933 14.5 72 2 volvo 145e (sw)
78 22.0 4 121.0 76 2511 18.0 72 2 volkswagen 411 (sw)
79 21.0 4 120.0 87 2979 19.5 72 2 peugeot 504 (sw)
80 26.0 4 96.0 69 2189 18.0 72 2 renault 12 (sw)
81 22.0 4 122.0 86 2395 16.0 72 1 ford pinto (sw)
82 28.0 4 97.0 92 2288 17.0 72 3 datsun 510 (sw)
83 23.0 4 120.0 97 2506 14.5 72 3 toyouta corona mark ii (sw)
84 28.0 4 98.0 80 2164 15.0 72 1 dodge colt (sw)
85 27.0 4 97.0 88 2100 16.5 72 3 toyota corolla 1600 (sw)
86 13.0 8 350.0 175 4100 13.0 73 1 buick century 350
87 14.0 8 304.0 150 3672 11.5 73 1 amc matador
88 13.0 8 350.0 145 3988 13.0 73 1 chevrolet malibu
89 14.0 8 302.0 137 4042 14.5 73 1 ford gran torino
90 15.0 8 318.0 150 3777 12.5 73 1 dodge coronet custom
91 12.0 8 429.0 198 4952 11.5 73 1 mercury marquis brougham
92 13.0 8 400.0 150 4464 12.0 73 1 chevrolet caprice classic
93 13.0 8 351.0 158 4363 13.0 73 1 ford ltd
94 14.0 8 318.0 150 4237 14.5 73 1 plymouth fury gran sedan
95 13.0 8 440.0 215 4735 11.0 73 1 chrysler new yorker brougham
96 12.0 8 455.0 225 4951 11.0 73 1 buick electra 225 custom
97 13.0 8 360.0 175 3821 11.0 73 1 amc ambassador brougham
98 18.0 6 225.0 105 3121 16.5 73 1 plymouth valiant
99 16.0 6 250.0 100 3278 18.0 73 1 chevrolet nova custom
100 18.0 6 232.0 100 2945 16.0 73 1 amc hornet
101 18.0 6 250.0 88 3021 16.5 73 1 ford maverick
102 23.0 6 198.0 95 2904 16.0 73 1 plymouth duster
103 26.0 4 97.0 46 1950 21.0 73 2 volkswagen super beetle
104 11.0 8 400.0 150 4997 14.0 73 1 chevrolet impala
105 12.0 8 400.0 167 4906 12.5 73 1 ford country
106 13.0 8 360.0 170 4654 13.0 73 1 plymouth custom suburb
107 12.0 8 350.0 180 4499 12.5 73 1 oldsmobile vista cruiser
108 18.0 6 232.0 100 2789 15.0 73 1 amc gremlin
109 20.0 4 97.0 88 2279 19.0 73 3 toyota carina
110 21.0 4 140.0 72 2401 19.5 73 1 chevrolet vega
111 22.0 4 108.0 94 2379 16.5 73 3 datsun 610
112 18.0 3 70.0 90 2124 13.5 73 3 maxda rx3
113 19.0 4 122.0 85 2310 18.5 73 1 ford pinto
114 21.0 6 155.0 107 2472 14.0 73 1 mercury capri v6
115 26.0 4 98.0 90 2265 15.5 73 2 fiat 124 sport coupe
116 15.0 8 350.0 145 4082 13.0 73 1 chevrolet monte carlo s
117 16.0 8 400.0 230 4278 9.5 73 1 pontiac grand prix
118 29.0 4 68.0 49 1867 19.5 73 2 fiat 128
119 24.0 4 116.0 75 2158 15.5 73 2 opel manta
120 20.0 4 114.0 91 2582 14.0 73 2 audi 100ls
121 19.0 4 121.0 112 2868 15.5 73 2 volvo 144ea
122 15.0 8 318.0 150 3399 11.0 73 1 dodge dart custom
123 24.0 4 121.0 110 2660 14.0 73 2 saab 99le
124 20.0 6 156.0 122 2807 13.5 73 3 toyota mark ii
125 11.0 8 350.0 180 3664 11.0 73 1 oldsmobile omega
126 20.0 6 198.0 95 3102 16.5 74 1 plymouth duster
128 19.0 6 232.0 100 2901 16.0 74 1 amc hornet
129 15.0 6 250.0 100 3336 17.0 74 1 chevrolet nova
130 31.0 4 79.0 67 1950 19.0 74 3 datsun b210
131 26.0 4 122.0 80 2451 16.5 74 1 ford pinto
132 32.0 4 71.0 65 1836 21.0 74 3 toyota corolla 1200
133 25.0 4 140.0 75 2542 17.0 74 1 chevrolet vega
134 16.0 6 250.0 100 3781 17.0 74 1 chevrolet chevelle malibu classic
135 16.0 6 258.0 110 3632 18.0 74 1 amc matador
136 18.0 6 225.0 105 3613 16.5 74 1 plymouth satellite sebring
137 16.0 8 302.0 140 4141 14.0 74 1 ford gran torino
138 13.0 8 350.0 150 4699 14.5 74 1 buick century luxus (sw)
139 14.0 8 318.0 150 4457 13.5 74 1 dodge coronet custom (sw)
140 14.0 8 302.0 140 4638 16.0 74 1 ford gran torino (sw)
141 14.0 8 304.0 150 4257 15.5 74 1 amc matador (sw)
142 29.0 4 98.0 83 2219 16.5 74 2 audi fox
143 26.0 4 79.0 67 1963 15.5 74 2 volkswagen dasher
144 26.0 4 97.0 78 2300 14.5 74 2 opel manta
145 31.0 4 76.0 52 1649 16.5 74 3 toyota corona
146 32.0 4 83.0 61 2003 19.0 74 3 datsun 710
147 28.0 4 90.0 75 2125 14.5 74 1 dodge colt
148 24.0 4 90.0 75 2108 15.5 74 2 fiat 128
149 26.0 4 116.0 75 2246 14.0 74 2 fiat 124 tc
150 24.0 4 120.0 97 2489 15.0 74 3 honda civic
151 26.0 4 108.0 93 2391 15.5 74 3 subaru
152 31.0 4 79.0 67 2000 16.0 74 2 fiat x1.9
153 19.0 6 225.0 95 3264 16.0 75 1 plymouth valiant custom
154 18.0 6 250.0 105 3459 16.0 75 1 chevrolet nova
155 15.0 6 250.0 72 3432 21.0 75 1 mercury monarch
156 15.0 6 250.0 72 3158 19.5 75 1 ford maverick
157 16.0 8 400.0 170 4668 11.5 75 1 pontiac catalina
158 15.0 8 350.0 145 4440 14.0 75 1 chevrolet bel air
159 16.0 8 318.0 150 4498 14.5 75 1 plymouth grand fury
160 14.0 8 351.0 148 4657 13.5 75 1 ford ltd
161 17.0 6 231.0 110 3907 21.0 75 1 buick century
162 16.0 6 250.0 105 3897 18.5 75 1 chevroelt chevelle malibu
163 15.0 6 258.0 110 3730 19.0 75 1 amc matador
164 18.0 6 225.0 95 3785 19.0 75 1 plymouth fury
165 21.0 6 231.0 110 3039 15.0 75 1 buick skyhawk
166 20.0 8 262.0 110 3221 13.5 75 1 chevrolet monza 2+2
167 13.0 8 302.0 129 3169 12.0 75 1 ford mustang ii
168 29.0 4 97.0 75 2171 16.0 75 3 toyota corolla
169 23.0 4 140.0 83 2639 17.0 75 1 ford pinto
170 20.0 6 232.0 100 2914 16.0 75 1 amc gremlin
171 23.0 4 140.0 78 2592 18.5 75 1 pontiac astro
172 24.0 4 134.0 96 2702 13.5 75 3 toyota corona
173 25.0 4 90.0 71 2223 16.5 75 2 volkswagen dasher
174 24.0 4 119.0 97 2545 17.0 75 3 datsun 710
175 18.0 6 171.0 97 2984 14.5 75 1 ford pinto
176 29.0 4 90.0 70 1937 14.0 75 2 volkswagen rabbit
177 19.0 6 232.0 90 3211 17.0 75 1 amc pacer
178 23.0 4 115.0 95 2694 15.0 75 2 audi 100ls
179 23.0 4 120.0 88 2957 17.0 75 2 peugeot 504
180 22.0 4 121.0 98 2945 14.5 75 2 volvo 244dl
181 25.0 4 121.0 115 2671 13.5 75 2 saab 99le
182 33.0 4 91.0 53 1795 17.5 75 3 honda civic cvcc
183 28.0 4 107.0 86 2464 15.5 76 2 fiat 131
184 25.0 4 116.0 81 2220 16.9 76 2 opel 1900
185 25.0 4 140.0 92 2572 14.9 76 1 capri ii
186 26.0 4 98.0 79 2255 17.7 76 1 dodge colt
187 27.0 4 101.0 83 2202 15.3 76 2 renault 12tl
188 17.5 8 305.0 140 4215 13.0 76 1 chevrolet chevelle malibu classic
189 16.0 8 318.0 150 4190 13.0 76 1 dodge coronet brougham
190 15.5 8 304.0 120 3962 13.9 76 1 amc matador
191 14.5 8 351.0 152 4215 12.8 76 1 ford gran torino
192 22.0 6 225.0 100 3233 15.4 76 1 plymouth valiant
193 22.0 6 250.0 105 3353 14.5 76 1 chevrolet nova
194 24.0 6 200.0 81 3012 17.6 76 1 ford maverick
195 22.5 6 232.0 90 3085 17.6 76 1 amc hornet
196 29.0 4 85.0 52 2035 22.2 76 1 chevrolet chevette
197 24.5 4 98.0 60 2164 22.1 76 1 chevrolet woody
198 29.0 4 90.0 70 1937 14.2 76 2 vw rabbit
199 33.0 4 91.0 53 1795 17.4 76 3 honda civic
200 20.0 6 225.0 100 3651 17.7 76 1 dodge aspen se
201 18.0 6 250.0 78 3574 21.0 76 1 ford granada ghia
202 18.5 6 250.0 110 3645 16.2 76 1 pontiac ventura sj
203 17.5 6 258.0 95 3193 17.8 76 1 amc pacer d/l
204 29.5 4 97.0 71 1825 12.2 76 2 volkswagen rabbit
205 32.0 4 85.0 70 1990 17.0 76 3 datsun b-210
206 28.0 4 97.0 75 2155 16.4 76 3 toyota corolla
207 26.5 4 140.0 72 2565 13.6 76 1 ford pinto
208 20.0 4 130.0 102 3150 15.7 76 2 volvo 245
209 13.0 8 318.0 150 3940 13.2 76 1 plymouth volare premier v8
210 19.0 4 120.0 88 3270 21.9 76 2 peugeot 504
211 19.0 6 156.0 108 2930 15.5 76 3 toyota mark ii
212 16.5 6 168.0 120 3820 16.7 76 2 mercedes-benz 280s
213 16.5 8 350.0 180 4380 12.1 76 1 cadillac seville
214 13.0 8 350.0 145 4055 12.0 76 1 chevy c10
215 13.0 8 302.0 130 3870 15.0 76 1 ford f108
216 13.0 8 318.0 150 3755 14.0 76 1 dodge d100
217 31.5 4 98.0 68 2045 18.5 77 3 honda accord cvcc
218 30.0 4 111.0 80 2155 14.8 77 1 buick opel isuzu deluxe
219 36.0 4 79.0 58 1825 18.6 77 2 renault 5 gtl
220 25.5 4 122.0 96 2300 15.5 77 1 plymouth arrow gs
221 33.5 4 85.0 70 1945 16.8 77 3 datsun f-10 hatchback
222 17.5 8 305.0 145 3880 12.5 77 1 chevrolet caprice classic
223 17.0 8 260.0 110 4060 19.0 77 1 oldsmobile cutlass supreme
224 15.5 8 318.0 145 4140 13.7 77 1 dodge monaco brougham
225 15.0 8 302.0 130 4295 14.9 77 1 mercury cougar brougham
226 17.5 6 250.0 110 3520 16.4 77 1 chevrolet concours
227 20.5 6 231.0 105 3425 16.9 77 1 buick skylark
228 19.0 6 225.0 100 3630 17.7 77 1 plymouth volare custom
229 18.5 6 250.0 98 3525 19.0 77 1 ford granada
230 16.0 8 400.0 180 4220 11.1 77 1 pontiac grand prix lj
231 15.5 8 350.0 170 4165 11.4 77 1 chevrolet monte carlo landau
232 15.5 8 400.0 190 4325 12.2 77 1 chrysler cordoba
233 16.0 8 351.0 149 4335 14.5 77 1 ford thunderbird
234 29.0 4 97.0 78 1940 14.5 77 2 volkswagen rabbit custom
235 24.5 4 151.0 88 2740 16.0 77 1 pontiac sunbird coupe
236 26.0 4 97.0 75 2265 18.2 77 3 toyota corolla liftback
237 25.5 4 140.0 89 2755 15.8 77 1 ford mustang ii 2+2
238 30.5 4 98.0 63 2051 17.0 77 1 chevrolet chevette
239 33.5 4 98.0 83 2075 15.9 77 1 dodge colt m/m
240 30.0 4 97.0 67 1985 16.4 77 3 subaru dl
241 30.5 4 97.0 78 2190 14.1 77 2 volkswagen dasher
242 22.0 6 146.0 97 2815 14.5 77 3 datsun 810
243 21.5 4 121.0 110 2600 12.8 77 2 bmw 320i
244 21.5 3 80.0 110 2720 13.5 77 3 mazda rx-4
245 43.1 4 90.0 48 1985 21.5 78 2 volkswagen rabbit custom diesel
246 36.1 4 98.0 66 1800 14.4 78 1 ford fiesta
247 32.8 4 78.0 52 1985 19.4 78 3 mazda glc deluxe
248 39.4 4 85.0 70 2070 18.6 78 3 datsun b210 gx
249 36.1 4 91.0 60 1800 16.4 78 3 honda civic cvcc
250 19.9 8 260.0 110 3365 15.5 78 1 oldsmobile cutlass salon brougham
251 19.4 8 318.0 140 3735 13.2 78 1 dodge diplomat
252 20.2 8 302.0 139 3570 12.8 78 1 mercury monarch ghia
253 19.2 6 231.0 105 3535 19.2 78 1 pontiac phoenix lj
254 20.5 6 200.0 95 3155 18.2 78 1 chevrolet malibu
255 20.2 6 200.0 85 2965 15.8 78 1 ford fairmont (auto)
256 25.1 4 140.0 88 2720 15.4 78 1 ford fairmont (man)
257 20.5 6 225.0 100 3430 17.2 78 1 plymouth volare
258 19.4 6 232.0 90 3210 17.2 78 1 amc concord
259 20.6 6 231.0 105 3380 15.8 78 1 buick century special
260 20.8 6 200.0 85 3070 16.7 78 1 mercury zephyr
261 18.6 6 225.0 110 3620 18.7 78 1 dodge aspen
262 18.1 6 258.0 120 3410 15.1 78 1 amc concord d/l
263 19.2 8 305.0 145 3425 13.2 78 1 chevrolet monte carlo landau
264 17.7 6 231.0 165 3445 13.4 78 1 buick regal sport coupe (turbo)
265 18.1 8 302.0 139 3205 11.2 78 1 ford futura
266 17.5 8 318.0 140 4080 13.7 78 1 dodge magnum xe
267 30.0 4 98.0 68 2155 16.5 78 1 chevrolet chevette
268 27.5 4 134.0 95 2560 14.2 78 3 toyota corona
269 27.2 4 119.0 97 2300 14.7 78 3 datsun 510
270 30.9 4 105.0 75 2230 14.5 78 1 dodge omni
271 21.1 4 134.0 95 2515 14.8 78 3 toyota celica gt liftback
272 23.2 4 156.0 105 2745 16.7 78 1 plymouth sapporo
273 23.8 4 151.0 85 2855 17.6 78 1 oldsmobile starfire sx
274 23.9 4 119.0 97 2405 14.9 78 3 datsun 200-sx
275 20.3 5 131.0 103 2830 15.9 78 2 audi 5000
276 17.0 6 163.0 125 3140 13.6 78 2 volvo 264gl
277 21.6 4 121.0 115 2795 15.7 78 2 saab 99gle
278 16.2 6 163.0 133 3410 15.8 78 2 peugeot 604sl
279 31.5 4 89.0 71 1990 14.9 78 2 volkswagen scirocco
280 29.5 4 98.0 68 2135 16.6 78 3 honda accord lx
281 21.5 6 231.0 115 3245 15.4 79 1 pontiac lemans v6
282 19.8 6 200.0 85 2990 18.2 79 1 mercury zephyr 6
283 22.3 4 140.0 88 2890 17.3 79 1 ford fairmont 4
284 20.2 6 232.0 90 3265 18.2 79 1 amc concord dl 6
285 20.6 6 225.0 110 3360 16.6 79 1 dodge aspen 6
286 17.0 8 305.0 130 3840 15.4 79 1 chevrolet caprice classic
287 17.6 8 302.0 129 3725 13.4 79 1 ford ltd landau
288 16.5 8 351.0 138 3955 13.2 79 1 mercury grand marquis
289 18.2 8 318.0 135 3830 15.2 79 1 dodge st. regis
290 16.9 8 350.0 155 4360 14.9 79 1 buick estate wagon (sw)
291 15.5 8 351.0 142 4054 14.3 79 1 ford country squire (sw)
292 19.2 8 267.0 125 3605 15.0 79 1 chevrolet malibu classic (sw)
293 18.5 8 360.0 150 3940 13.0 79 1 chrysler lebaron town @ country (sw)
294 31.9 4 89.0 71 1925 14.0 79 2 vw rabbit custom
295 34.1 4 86.0 65 1975 15.2 79 3 maxda glc deluxe
296 35.7 4 98.0 80 1915 14.4 79 1 dodge colt hatchback custom
297 27.4 4 121.0 80 2670 15.0 79 1 amc spirit dl
298 25.4 5 183.0 77 3530 20.1 79 2 mercedes benz 300d
299 23.0 8 350.0 125 3900 17.4 79 1 cadillac eldorado
300 27.2 4 141.0 71 3190 24.8 79 2 peugeot 504
301 23.9 8 260.0 90 3420 22.2 79 1 oldsmobile cutlass salon brougham
302 34.2 4 105.0 70 2200 13.2 79 1 plymouth horizon
303 34.5 4 105.0 70 2150 14.9 79 1 plymouth horizon tc3
304 31.8 4 85.0 65 2020 19.2 79 3 datsun 210
305 37.3 4 91.0 69 2130 14.7 79 2 fiat strada custom
306 28.4 4 151.0 90 2670 16.0 79 1 buick skylark limited
307 28.8 6 173.0 115 2595 11.3 79 1 chevrolet citation
308 26.8 6 173.0 115 2700 12.9 79 1 oldsmobile omega brougham
309 33.5 4 151.0 90 2556 13.2 79 1 pontiac phoenix
310 41.5 4 98.0 76 2144 14.7 80 2 vw rabbit
311 38.1 4 89.0 60 1968 18.8 80 3 toyota corolla tercel
312 32.1 4 98.0 70 2120 15.5 80 1 chevrolet chevette
313 37.2 4 86.0 65 2019 16.4 80 3 datsun 310
314 28.0 4 151.0 90 2678 16.5 80 1 chevrolet citation
315 26.4 4 140.0 88 2870 18.1 80 1 ford fairmont
316 24.3 4 151.0 90 3003 20.1 80 1 amc concord
317 19.1 6 225.0 90 3381 18.7 80 1 dodge aspen
318 34.3 4 97.0 78 2188 15.8 80 2 audi 4000
319 29.8 4 134.0 90 2711 15.5 80 3 toyota corona liftback
320 31.3 4 120.0 75 2542 17.5 80 3 mazda 626
321 37.0 4 119.0 92 2434 15.0 80 3 datsun 510 hatchback
322 32.2 4 108.0 75 2265 15.2 80 3 toyota corolla
323 46.6 4 86.0 65 2110 17.9 80 3 mazda glc
324 27.9 4 156.0 105 2800 14.4 80 1 dodge colt
325 40.8 4 85.0 65 2110 19.2 80 3 datsun 210
326 44.3 4 90.0 48 2085 21.7 80 2 vw rabbit c (diesel)
327 43.4 4 90.0 48 2335 23.7 80 2 vw dasher (diesel)
328 36.4 5 121.0 67 2950 19.9 80 2 audi 5000s (diesel)
329 30.0 4 146.0 67 3250 21.8 80 2 mercedes-benz 240d
330 44.6 4 91.0 67 1850 13.8 80 3 honda civic 1500 gl
332 33.8 4 97.0 67 2145 18.0 80 3 subaru dl
333 29.8 4 89.0 62 1845 15.3 80 2 vokswagen rabbit
334 32.7 6 168.0 132 2910 11.4 80 3 datsun 280-zx
335 23.7 3 70.0 100 2420 12.5 80 3 mazda rx-7 gs
336 35.0 4 122.0 88 2500 15.1 80 2 triumph tr7 coupe
338 32.4 4 107.0 72 2290 17.0 80 3 honda accord
339 27.2 4 135.0 84 2490 15.7 81 1 plymouth reliant
340 26.6 4 151.0 84 2635 16.4 81 1 buick skylark
341 25.8 4 156.0 92 2620 14.4 81 1 dodge aries wagon (sw)
342 23.5 6 173.0 110 2725 12.6 81 1 chevrolet citation
343 30.0 4 135.0 84 2385 12.9 81 1 plymouth reliant
344 39.1 4 79.0 58 1755 16.9 81 3 toyota starlet
345 39.0 4 86.0 64 1875 16.4 81 1 plymouth champ
346 35.1 4 81.0 60 1760 16.1 81 3 honda civic 1300
347 32.3 4 97.0 67 2065 17.8 81 3 subaru
348 37.0 4 85.0 65 1975 19.4 81 3 datsun 210 mpg
349 37.7 4 89.0 62 2050 17.3 81 3 toyota tercel
350 34.1 4 91.0 68 1985 16.0 81 3 mazda glc 4
351 34.7 4 105.0 63 2215 14.9 81 1 plymouth horizon 4
352 34.4 4 98.0 65 2045 16.2 81 1 ford escort 4w
353 29.9 4 98.0 65 2380 20.7 81 1 ford escort 2h
354 33.0 4 105.0 74 2190 14.2 81 2 volkswagen jetta
356 33.7 4 107.0 75 2210 14.4 81 3 honda prelude
357 32.4 4 108.0 75 2350 16.8 81 3 toyota corolla
358 32.9 4 119.0 100 2615 14.8 81 3 datsun 200sx
359 31.6 4 120.0 74 2635 18.3 81 3 mazda 626
360 28.1 4 141.0 80 3230 20.4 81 2 peugeot 505s turbo diesel
361 30.7 6 145.0 76 3160 19.6 81 2 volvo diesel
362 25.4 6 168.0 116 2900 12.6 81 3 toyota cressida
363 24.2 6 146.0 120 2930 13.8 81 3 datsun 810 maxima
364 22.4 6 231.0 110 3415 15.8 81 1 buick century
365 26.6 8 350.0 105 3725 19.0 81 1 oldsmobile cutlass ls
366 20.2 6 200.0 88 3060 17.1 81 1 ford granada gl
367 17.6 6 225.0 85 3465 16.6 81 1 chrysler lebaron salon
368 28.0 4 112.0 88 2605 19.6 82 1 chevrolet cavalier
369 27.0 4 112.0 88 2640 18.6 82 1 chevrolet cavalier wagon
370 34.0 4 112.0 88 2395 18.0 82 1 chevrolet cavalier 2-door
371 31.0 4 112.0 85 2575 16.2 82 1 pontiac j2000 se hatchback
372 29.0 4 135.0 84 2525 16.0 82 1 dodge aries se
373 27.0 4 151.0 90 2735 18.0 82 1 pontiac phoenix
374 24.0 4 140.0 92 2865 16.4 82 1 ford fairmont futura
375 36.0 4 105.0 74 1980 15.3 82 2 volkswagen rabbit l
376 37.0 4 91.0 68 2025 18.2 82 3 mazda glc custom l
377 31.0 4 91.0 68 1970 17.6 82 3 mazda glc custom
378 38.0 4 105.0 63 2125 14.7 82 1 plymouth horizon miser
379 36.0 4 98.0 70 2125 17.3 82 1 mercury lynx l
380 36.0 4 120.0 88 2160 14.5 82 3 nissan stanza xe
381 36.0 4 107.0 75 2205 14.5 82 3 honda accord
382 34.0 4 108.0 70 2245 16.9 82 3 toyota corolla
383 38.0 4 91.0 67 1965 15.0 82 3 honda civic
384 32.0 4 91.0 67 1965 15.7 82 3 honda civic (auto)
385 38.0 4 91.0 67 1995 16.2 82 3 datsun 310 gx
386 25.0 6 181.0 110 2945 16.4 82 1 buick century limited
387 38.0 6 262.0 85 3015 17.0 82 1 oldsmobile cutlass ciera (diesel)
388 26.0 4 156.0 92 2585 14.5 82 1 chrysler lebaron medallion
389 22.0 6 232.0 112 2835 14.7 82 1 ford granada l
390 32.0 4 144.0 96 2665 13.9 82 3 toyota celica gt
391 36.0 4 135.0 84 2370 13.0 82 1 dodge charger 2.2
392 27.0 4 151.0 90 2950 17.3 82 1 chevrolet camaro
393 27.0 4 140.0 86 2790 15.6 82 1 ford mustang gl
394 44.0 4 97.0 52 2130 24.6 82 2 vw pickup
395 32.0 4 135.0 84 2295 11.6 82 1 dodge rampage
396 28.0 4 120.0 79 2625 18.6 82 1 ford ranger
397 31.0 4 119.0 82 2720 19.4 82 1 chevy s-10
class(Auto)
## [1] "data.frame"
dim(Auto)
## [1] 392   9
names(Auto)
## [1] "mpg"          "cylinders"    "displacement" "horsepower"   "weight"      
## [6] "acceleration" "year"         "origin"       "name"
str(Auto)
## 'data.frame':    392 obs. of  9 variables:
##  $ mpg         : num  18 15 18 16 17 15 14 14 14 15 ...
##  $ cylinders   : num  8 8 8 8 8 8 8 8 8 8 ...
##  $ displacement: num  307 350 318 304 302 429 454 440 455 390 ...
##  $ horsepower  : num  130 165 150 150 140 198 220 215 225 190 ...
##  $ weight      : num  3504 3693 3436 3433 3449 ...
##  $ acceleration: num  12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
##  $ year        : num  70 70 70 70 70 70 70 70 70 70 ...
##  $ origin      : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ name        : Factor w/ 304 levels "amc ambassador brougham",..: 49 36 231 14 161 141 54 223 241 2 ...
na.omit(Auto)
##      mpg cylinders displacement horsepower weight acceleration year origin
## 1   18.0         8        307.0        130   3504         12.0   70      1
## 2   15.0         8        350.0        165   3693         11.5   70      1
## 3   18.0         8        318.0        150   3436         11.0   70      1
## 4   16.0         8        304.0        150   3433         12.0   70      1
## 5   17.0         8        302.0        140   3449         10.5   70      1
## 6   15.0         8        429.0        198   4341         10.0   70      1
## 7   14.0         8        454.0        220   4354          9.0   70      1
## 8   14.0         8        440.0        215   4312          8.5   70      1
## 9   14.0         8        455.0        225   4425         10.0   70      1
## 10  15.0         8        390.0        190   3850          8.5   70      1
## 11  15.0         8        383.0        170   3563         10.0   70      1
## 12  14.0         8        340.0        160   3609          8.0   70      1
## 13  15.0         8        400.0        150   3761          9.5   70      1
## 14  14.0         8        455.0        225   3086         10.0   70      1
## 15  24.0         4        113.0         95   2372         15.0   70      3
## 16  22.0         6        198.0         95   2833         15.5   70      1
## 17  18.0         6        199.0         97   2774         15.5   70      1
## 18  21.0         6        200.0         85   2587         16.0   70      1
## 19  27.0         4         97.0         88   2130         14.5   70      3
## 20  26.0         4         97.0         46   1835         20.5   70      2
## 21  25.0         4        110.0         87   2672         17.5   70      2
## 22  24.0         4        107.0         90   2430         14.5   70      2
## 23  25.0         4        104.0         95   2375         17.5   70      2
## 24  26.0         4        121.0        113   2234         12.5   70      2
## 25  21.0         6        199.0         90   2648         15.0   70      1
## 26  10.0         8        360.0        215   4615         14.0   70      1
## 27  10.0         8        307.0        200   4376         15.0   70      1
## 28  11.0         8        318.0        210   4382         13.5   70      1
## 29   9.0         8        304.0        193   4732         18.5   70      1
## 30  27.0         4         97.0         88   2130         14.5   71      3
## 31  28.0         4        140.0         90   2264         15.5   71      1
## 32  25.0         4        113.0         95   2228         14.0   71      3
## 34  19.0         6        232.0        100   2634         13.0   71      1
## 35  16.0         6        225.0        105   3439         15.5   71      1
## 36  17.0         6        250.0        100   3329         15.5   71      1
## 37  19.0         6        250.0         88   3302         15.5   71      1
## 38  18.0         6        232.0        100   3288         15.5   71      1
## 39  14.0         8        350.0        165   4209         12.0   71      1
## 40  14.0         8        400.0        175   4464         11.5   71      1
## 41  14.0         8        351.0        153   4154         13.5   71      1
## 42  14.0         8        318.0        150   4096         13.0   71      1
## 43  12.0         8        383.0        180   4955         11.5   71      1
## 44  13.0         8        400.0        170   4746         12.0   71      1
## 45  13.0         8        400.0        175   5140         12.0   71      1
## 46  18.0         6        258.0        110   2962         13.5   71      1
## 47  22.0         4        140.0         72   2408         19.0   71      1
## 48  19.0         6        250.0        100   3282         15.0   71      1
## 49  18.0         6        250.0         88   3139         14.5   71      1
## 50  23.0         4        122.0         86   2220         14.0   71      1
## 51  28.0         4        116.0         90   2123         14.0   71      2
## 52  30.0         4         79.0         70   2074         19.5   71      2
## 53  30.0         4         88.0         76   2065         14.5   71      2
## 54  31.0         4         71.0         65   1773         19.0   71      3
## 55  35.0         4         72.0         69   1613         18.0   71      3
## 56  27.0         4         97.0         60   1834         19.0   71      2
## 57  26.0         4         91.0         70   1955         20.5   71      1
## 58  24.0         4        113.0         95   2278         15.5   72      3
## 59  25.0         4         97.5         80   2126         17.0   72      1
## 60  23.0         4         97.0         54   2254         23.5   72      2
## 61  20.0         4        140.0         90   2408         19.5   72      1
## 62  21.0         4        122.0         86   2226         16.5   72      1
## 63  13.0         8        350.0        165   4274         12.0   72      1
## 64  14.0         8        400.0        175   4385         12.0   72      1
## 65  15.0         8        318.0        150   4135         13.5   72      1
## 66  14.0         8        351.0        153   4129         13.0   72      1
## 67  17.0         8        304.0        150   3672         11.5   72      1
## 68  11.0         8        429.0        208   4633         11.0   72      1
## 69  13.0         8        350.0        155   4502         13.5   72      1
## 70  12.0         8        350.0        160   4456         13.5   72      1
## 71  13.0         8        400.0        190   4422         12.5   72      1
## 72  19.0         3         70.0         97   2330         13.5   72      3
## 73  15.0         8        304.0        150   3892         12.5   72      1
## 74  13.0         8        307.0        130   4098         14.0   72      1
## 75  13.0         8        302.0        140   4294         16.0   72      1
## 76  14.0         8        318.0        150   4077         14.0   72      1
## 77  18.0         4        121.0        112   2933         14.5   72      2
## 78  22.0         4        121.0         76   2511         18.0   72      2
## 79  21.0         4        120.0         87   2979         19.5   72      2
## 80  26.0         4         96.0         69   2189         18.0   72      2
## 81  22.0         4        122.0         86   2395         16.0   72      1
## 82  28.0         4         97.0         92   2288         17.0   72      3
## 83  23.0         4        120.0         97   2506         14.5   72      3
## 84  28.0         4         98.0         80   2164         15.0   72      1
## 85  27.0         4         97.0         88   2100         16.5   72      3
## 86  13.0         8        350.0        175   4100         13.0   73      1
## 87  14.0         8        304.0        150   3672         11.5   73      1
## 88  13.0         8        350.0        145   3988         13.0   73      1
## 89  14.0         8        302.0        137   4042         14.5   73      1
## 90  15.0         8        318.0        150   3777         12.5   73      1
## 91  12.0         8        429.0        198   4952         11.5   73      1
## 92  13.0         8        400.0        150   4464         12.0   73      1
## 93  13.0         8        351.0        158   4363         13.0   73      1
## 94  14.0         8        318.0        150   4237         14.5   73      1
## 95  13.0         8        440.0        215   4735         11.0   73      1
## 96  12.0         8        455.0        225   4951         11.0   73      1
## 97  13.0         8        360.0        175   3821         11.0   73      1
## 98  18.0         6        225.0        105   3121         16.5   73      1
## 99  16.0         6        250.0        100   3278         18.0   73      1
## 100 18.0         6        232.0        100   2945         16.0   73      1
## 101 18.0         6        250.0         88   3021         16.5   73      1
## 102 23.0         6        198.0         95   2904         16.0   73      1
## 103 26.0         4         97.0         46   1950         21.0   73      2
## 104 11.0         8        400.0        150   4997         14.0   73      1
## 105 12.0         8        400.0        167   4906         12.5   73      1
## 106 13.0         8        360.0        170   4654         13.0   73      1
## 107 12.0         8        350.0        180   4499         12.5   73      1
## 108 18.0         6        232.0        100   2789         15.0   73      1
## 109 20.0         4         97.0         88   2279         19.0   73      3
## 110 21.0         4        140.0         72   2401         19.5   73      1
## 111 22.0         4        108.0         94   2379         16.5   73      3
## 112 18.0         3         70.0         90   2124         13.5   73      3
## 113 19.0         4        122.0         85   2310         18.5   73      1
## 114 21.0         6        155.0        107   2472         14.0   73      1
## 115 26.0         4         98.0         90   2265         15.5   73      2
## 116 15.0         8        350.0        145   4082         13.0   73      1
## 117 16.0         8        400.0        230   4278          9.5   73      1
## 118 29.0         4         68.0         49   1867         19.5   73      2
## 119 24.0         4        116.0         75   2158         15.5   73      2
## 120 20.0         4        114.0         91   2582         14.0   73      2
## 121 19.0         4        121.0        112   2868         15.5   73      2
## 122 15.0         8        318.0        150   3399         11.0   73      1
## 123 24.0         4        121.0        110   2660         14.0   73      2
## 124 20.0         6        156.0        122   2807         13.5   73      3
## 125 11.0         8        350.0        180   3664         11.0   73      1
## 126 20.0         6        198.0         95   3102         16.5   74      1
## 128 19.0         6        232.0        100   2901         16.0   74      1
## 129 15.0         6        250.0        100   3336         17.0   74      1
## 130 31.0         4         79.0         67   1950         19.0   74      3
## 131 26.0         4        122.0         80   2451         16.5   74      1
## 132 32.0         4         71.0         65   1836         21.0   74      3
## 133 25.0         4        140.0         75   2542         17.0   74      1
## 134 16.0         6        250.0        100   3781         17.0   74      1
## 135 16.0         6        258.0        110   3632         18.0   74      1
## 136 18.0         6        225.0        105   3613         16.5   74      1
## 137 16.0         8        302.0        140   4141         14.0   74      1
## 138 13.0         8        350.0        150   4699         14.5   74      1
## 139 14.0         8        318.0        150   4457         13.5   74      1
## 140 14.0         8        302.0        140   4638         16.0   74      1
## 141 14.0         8        304.0        150   4257         15.5   74      1
## 142 29.0         4         98.0         83   2219         16.5   74      2
## 143 26.0         4         79.0         67   1963         15.5   74      2
## 144 26.0         4         97.0         78   2300         14.5   74      2
## 145 31.0         4         76.0         52   1649         16.5   74      3
## 146 32.0         4         83.0         61   2003         19.0   74      3
## 147 28.0         4         90.0         75   2125         14.5   74      1
## 148 24.0         4         90.0         75   2108         15.5   74      2
## 149 26.0         4        116.0         75   2246         14.0   74      2
## 150 24.0         4        120.0         97   2489         15.0   74      3
## 151 26.0         4        108.0         93   2391         15.5   74      3
## 152 31.0         4         79.0         67   2000         16.0   74      2
## 153 19.0         6        225.0         95   3264         16.0   75      1
## 154 18.0         6        250.0        105   3459         16.0   75      1
## 155 15.0         6        250.0         72   3432         21.0   75      1
## 156 15.0         6        250.0         72   3158         19.5   75      1
## 157 16.0         8        400.0        170   4668         11.5   75      1
## 158 15.0         8        350.0        145   4440         14.0   75      1
## 159 16.0         8        318.0        150   4498         14.5   75      1
## 160 14.0         8        351.0        148   4657         13.5   75      1
## 161 17.0         6        231.0        110   3907         21.0   75      1
## 162 16.0         6        250.0        105   3897         18.5   75      1
## 163 15.0         6        258.0        110   3730         19.0   75      1
## 164 18.0         6        225.0         95   3785         19.0   75      1
## 165 21.0         6        231.0        110   3039         15.0   75      1
## 166 20.0         8        262.0        110   3221         13.5   75      1
## 167 13.0         8        302.0        129   3169         12.0   75      1
## 168 29.0         4         97.0         75   2171         16.0   75      3
## 169 23.0         4        140.0         83   2639         17.0   75      1
## 170 20.0         6        232.0        100   2914         16.0   75      1
## 171 23.0         4        140.0         78   2592         18.5   75      1
## 172 24.0         4        134.0         96   2702         13.5   75      3
## 173 25.0         4         90.0         71   2223         16.5   75      2
## 174 24.0         4        119.0         97   2545         17.0   75      3
## 175 18.0         6        171.0         97   2984         14.5   75      1
## 176 29.0         4         90.0         70   1937         14.0   75      2
## 177 19.0         6        232.0         90   3211         17.0   75      1
## 178 23.0         4        115.0         95   2694         15.0   75      2
## 179 23.0         4        120.0         88   2957         17.0   75      2
## 180 22.0         4        121.0         98   2945         14.5   75      2
## 181 25.0         4        121.0        115   2671         13.5   75      2
## 182 33.0         4         91.0         53   1795         17.5   75      3
## 183 28.0         4        107.0         86   2464         15.5   76      2
## 184 25.0         4        116.0         81   2220         16.9   76      2
## 185 25.0         4        140.0         92   2572         14.9   76      1
## 186 26.0         4         98.0         79   2255         17.7   76      1
## 187 27.0         4        101.0         83   2202         15.3   76      2
## 188 17.5         8        305.0        140   4215         13.0   76      1
## 189 16.0         8        318.0        150   4190         13.0   76      1
## 190 15.5         8        304.0        120   3962         13.9   76      1
## 191 14.5         8        351.0        152   4215         12.8   76      1
## 192 22.0         6        225.0        100   3233         15.4   76      1
## 193 22.0         6        250.0        105   3353         14.5   76      1
## 194 24.0         6        200.0         81   3012         17.6   76      1
## 195 22.5         6        232.0         90   3085         17.6   76      1
## 196 29.0         4         85.0         52   2035         22.2   76      1
## 197 24.5         4         98.0         60   2164         22.1   76      1
## 198 29.0         4         90.0         70   1937         14.2   76      2
## 199 33.0         4         91.0         53   1795         17.4   76      3
## 200 20.0         6        225.0        100   3651         17.7   76      1
## 201 18.0         6        250.0         78   3574         21.0   76      1
## 202 18.5         6        250.0        110   3645         16.2   76      1
## 203 17.5         6        258.0         95   3193         17.8   76      1
## 204 29.5         4         97.0         71   1825         12.2   76      2
## 205 32.0         4         85.0         70   1990         17.0   76      3
## 206 28.0         4         97.0         75   2155         16.4   76      3
## 207 26.5         4        140.0         72   2565         13.6   76      1
## 208 20.0         4        130.0        102   3150         15.7   76      2
## 209 13.0         8        318.0        150   3940         13.2   76      1
## 210 19.0         4        120.0         88   3270         21.9   76      2
## 211 19.0         6        156.0        108   2930         15.5   76      3
## 212 16.5         6        168.0        120   3820         16.7   76      2
## 213 16.5         8        350.0        180   4380         12.1   76      1
## 214 13.0         8        350.0        145   4055         12.0   76      1
## 215 13.0         8        302.0        130   3870         15.0   76      1
## 216 13.0         8        318.0        150   3755         14.0   76      1
## 217 31.5         4         98.0         68   2045         18.5   77      3
## 218 30.0         4        111.0         80   2155         14.8   77      1
## 219 36.0         4         79.0         58   1825         18.6   77      2
## 220 25.5         4        122.0         96   2300         15.5   77      1
## 221 33.5         4         85.0         70   1945         16.8   77      3
## 222 17.5         8        305.0        145   3880         12.5   77      1
## 223 17.0         8        260.0        110   4060         19.0   77      1
## 224 15.5         8        318.0        145   4140         13.7   77      1
## 225 15.0         8        302.0        130   4295         14.9   77      1
## 226 17.5         6        250.0        110   3520         16.4   77      1
## 227 20.5         6        231.0        105   3425         16.9   77      1
## 228 19.0         6        225.0        100   3630         17.7   77      1
## 229 18.5         6        250.0         98   3525         19.0   77      1
## 230 16.0         8        400.0        180   4220         11.1   77      1
## 231 15.5         8        350.0        170   4165         11.4   77      1
## 232 15.5         8        400.0        190   4325         12.2   77      1
## 233 16.0         8        351.0        149   4335         14.5   77      1
## 234 29.0         4         97.0         78   1940         14.5   77      2
## 235 24.5         4        151.0         88   2740         16.0   77      1
## 236 26.0         4         97.0         75   2265         18.2   77      3
## 237 25.5         4        140.0         89   2755         15.8   77      1
## 238 30.5         4         98.0         63   2051         17.0   77      1
## 239 33.5         4         98.0         83   2075         15.9   77      1
## 240 30.0         4         97.0         67   1985         16.4   77      3
## 241 30.5         4         97.0         78   2190         14.1   77      2
## 242 22.0         6        146.0         97   2815         14.5   77      3
## 243 21.5         4        121.0        110   2600         12.8   77      2
## 244 21.5         3         80.0        110   2720         13.5   77      3
## 245 43.1         4         90.0         48   1985         21.5   78      2
## 246 36.1         4         98.0         66   1800         14.4   78      1
## 247 32.8         4         78.0         52   1985         19.4   78      3
## 248 39.4         4         85.0         70   2070         18.6   78      3
## 249 36.1         4         91.0         60   1800         16.4   78      3
## 250 19.9         8        260.0        110   3365         15.5   78      1
## 251 19.4         8        318.0        140   3735         13.2   78      1
## 252 20.2         8        302.0        139   3570         12.8   78      1
## 253 19.2         6        231.0        105   3535         19.2   78      1
## 254 20.5         6        200.0         95   3155         18.2   78      1
## 255 20.2         6        200.0         85   2965         15.8   78      1
## 256 25.1         4        140.0         88   2720         15.4   78      1
## 257 20.5         6        225.0        100   3430         17.2   78      1
## 258 19.4         6        232.0         90   3210         17.2   78      1
## 259 20.6         6        231.0        105   3380         15.8   78      1
## 260 20.8         6        200.0         85   3070         16.7   78      1
## 261 18.6         6        225.0        110   3620         18.7   78      1
## 262 18.1         6        258.0        120   3410         15.1   78      1
## 263 19.2         8        305.0        145   3425         13.2   78      1
## 264 17.7         6        231.0        165   3445         13.4   78      1
## 265 18.1         8        302.0        139   3205         11.2   78      1
## 266 17.5         8        318.0        140   4080         13.7   78      1
## 267 30.0         4         98.0         68   2155         16.5   78      1
## 268 27.5         4        134.0         95   2560         14.2   78      3
## 269 27.2         4        119.0         97   2300         14.7   78      3
## 270 30.9         4        105.0         75   2230         14.5   78      1
## 271 21.1         4        134.0         95   2515         14.8   78      3
## 272 23.2         4        156.0        105   2745         16.7   78      1
## 273 23.8         4        151.0         85   2855         17.6   78      1
## 274 23.9         4        119.0         97   2405         14.9   78      3
## 275 20.3         5        131.0        103   2830         15.9   78      2
## 276 17.0         6        163.0        125   3140         13.6   78      2
## 277 21.6         4        121.0        115   2795         15.7   78      2
## 278 16.2         6        163.0        133   3410         15.8   78      2
## 279 31.5         4         89.0         71   1990         14.9   78      2
## 280 29.5         4         98.0         68   2135         16.6   78      3
## 281 21.5         6        231.0        115   3245         15.4   79      1
## 282 19.8         6        200.0         85   2990         18.2   79      1
## 283 22.3         4        140.0         88   2890         17.3   79      1
## 284 20.2         6        232.0         90   3265         18.2   79      1
## 285 20.6         6        225.0        110   3360         16.6   79      1
## 286 17.0         8        305.0        130   3840         15.4   79      1
## 287 17.6         8        302.0        129   3725         13.4   79      1
## 288 16.5         8        351.0        138   3955         13.2   79      1
## 289 18.2         8        318.0        135   3830         15.2   79      1
## 290 16.9         8        350.0        155   4360         14.9   79      1
## 291 15.5         8        351.0        142   4054         14.3   79      1
## 292 19.2         8        267.0        125   3605         15.0   79      1
## 293 18.5         8        360.0        150   3940         13.0   79      1
## 294 31.9         4         89.0         71   1925         14.0   79      2
## 295 34.1         4         86.0         65   1975         15.2   79      3
## 296 35.7         4         98.0         80   1915         14.4   79      1
## 297 27.4         4        121.0         80   2670         15.0   79      1
## 298 25.4         5        183.0         77   3530         20.1   79      2
## 299 23.0         8        350.0        125   3900         17.4   79      1
## 300 27.2         4        141.0         71   3190         24.8   79      2
## 301 23.9         8        260.0         90   3420         22.2   79      1
## 302 34.2         4        105.0         70   2200         13.2   79      1
## 303 34.5         4        105.0         70   2150         14.9   79      1
## 304 31.8         4         85.0         65   2020         19.2   79      3
## 305 37.3         4         91.0         69   2130         14.7   79      2
## 306 28.4         4        151.0         90   2670         16.0   79      1
## 307 28.8         6        173.0        115   2595         11.3   79      1
## 308 26.8         6        173.0        115   2700         12.9   79      1
## 309 33.5         4        151.0         90   2556         13.2   79      1
## 310 41.5         4         98.0         76   2144         14.7   80      2
## 311 38.1         4         89.0         60   1968         18.8   80      3
## 312 32.1         4         98.0         70   2120         15.5   80      1
## 313 37.2         4         86.0         65   2019         16.4   80      3
## 314 28.0         4        151.0         90   2678         16.5   80      1
## 315 26.4         4        140.0         88   2870         18.1   80      1
## 316 24.3         4        151.0         90   3003         20.1   80      1
## 317 19.1         6        225.0         90   3381         18.7   80      1
## 318 34.3         4         97.0         78   2188         15.8   80      2
## 319 29.8         4        134.0         90   2711         15.5   80      3
## 320 31.3         4        120.0         75   2542         17.5   80      3
## 321 37.0         4        119.0         92   2434         15.0   80      3
## 322 32.2         4        108.0         75   2265         15.2   80      3
## 323 46.6         4         86.0         65   2110         17.9   80      3
## 324 27.9         4        156.0        105   2800         14.4   80      1
## 325 40.8         4         85.0         65   2110         19.2   80      3
## 326 44.3         4         90.0         48   2085         21.7   80      2
## 327 43.4         4         90.0         48   2335         23.7   80      2
## 328 36.4         5        121.0         67   2950         19.9   80      2
## 329 30.0         4        146.0         67   3250         21.8   80      2
## 330 44.6         4         91.0         67   1850         13.8   80      3
## 332 33.8         4         97.0         67   2145         18.0   80      3
## 333 29.8         4         89.0         62   1845         15.3   80      2
## 334 32.7         6        168.0        132   2910         11.4   80      3
## 335 23.7         3         70.0        100   2420         12.5   80      3
## 336 35.0         4        122.0         88   2500         15.1   80      2
## 338 32.4         4        107.0         72   2290         17.0   80      3
## 339 27.2         4        135.0         84   2490         15.7   81      1
## 340 26.6         4        151.0         84   2635         16.4   81      1
## 341 25.8         4        156.0         92   2620         14.4   81      1
## 342 23.5         6        173.0        110   2725         12.6   81      1
## 343 30.0         4        135.0         84   2385         12.9   81      1
## 344 39.1         4         79.0         58   1755         16.9   81      3
## 345 39.0         4         86.0         64   1875         16.4   81      1
## 346 35.1         4         81.0         60   1760         16.1   81      3
## 347 32.3         4         97.0         67   2065         17.8   81      3
## 348 37.0         4         85.0         65   1975         19.4   81      3
## 349 37.7         4         89.0         62   2050         17.3   81      3
## 350 34.1         4         91.0         68   1985         16.0   81      3
## 351 34.7         4        105.0         63   2215         14.9   81      1
## 352 34.4         4         98.0         65   2045         16.2   81      1
## 353 29.9         4         98.0         65   2380         20.7   81      1
## 354 33.0         4        105.0         74   2190         14.2   81      2
## 356 33.7         4        107.0         75   2210         14.4   81      3
## 357 32.4         4        108.0         75   2350         16.8   81      3
## 358 32.9         4        119.0        100   2615         14.8   81      3
## 359 31.6         4        120.0         74   2635         18.3   81      3
## 360 28.1         4        141.0         80   3230         20.4   81      2
## 361 30.7         6        145.0         76   3160         19.6   81      2
## 362 25.4         6        168.0        116   2900         12.6   81      3
## 363 24.2         6        146.0        120   2930         13.8   81      3
## 364 22.4         6        231.0        110   3415         15.8   81      1
## 365 26.6         8        350.0        105   3725         19.0   81      1
## 366 20.2         6        200.0         88   3060         17.1   81      1
## 367 17.6         6        225.0         85   3465         16.6   81      1
## 368 28.0         4        112.0         88   2605         19.6   82      1
## 369 27.0         4        112.0         88   2640         18.6   82      1
## 370 34.0         4        112.0         88   2395         18.0   82      1
## 371 31.0         4        112.0         85   2575         16.2   82      1
## 372 29.0         4        135.0         84   2525         16.0   82      1
## 373 27.0         4        151.0         90   2735         18.0   82      1
## 374 24.0         4        140.0         92   2865         16.4   82      1
## 375 36.0         4        105.0         74   1980         15.3   82      2
## 376 37.0         4         91.0         68   2025         18.2   82      3
## 377 31.0         4         91.0         68   1970         17.6   82      3
## 378 38.0         4        105.0         63   2125         14.7   82      1
## 379 36.0         4         98.0         70   2125         17.3   82      1
## 380 36.0         4        120.0         88   2160         14.5   82      3
## 381 36.0         4        107.0         75   2205         14.5   82      3
## 382 34.0         4        108.0         70   2245         16.9   82      3
## 383 38.0         4         91.0         67   1965         15.0   82      3
## 384 32.0         4         91.0         67   1965         15.7   82      3
## 385 38.0         4         91.0         67   1995         16.2   82      3
## 386 25.0         6        181.0        110   2945         16.4   82      1
## 387 38.0         6        262.0         85   3015         17.0   82      1
## 388 26.0         4        156.0         92   2585         14.5   82      1
## 389 22.0         6        232.0        112   2835         14.7   82      1
## 390 32.0         4        144.0         96   2665         13.9   82      3
## 391 36.0         4        135.0         84   2370         13.0   82      1
## 392 27.0         4        151.0         90   2950         17.3   82      1
## 393 27.0         4        140.0         86   2790         15.6   82      1
## 394 44.0         4         97.0         52   2130         24.6   82      2
## 395 32.0         4        135.0         84   2295         11.6   82      1
## 396 28.0         4        120.0         79   2625         18.6   82      1
## 397 31.0         4        119.0         82   2720         19.4   82      1
##                                     name
## 1              chevrolet chevelle malibu
## 2                      buick skylark 320
## 3                     plymouth satellite
## 4                          amc rebel sst
## 5                            ford torino
## 6                       ford galaxie 500
## 7                       chevrolet impala
## 8                      plymouth fury iii
## 9                       pontiac catalina
## 10                    amc ambassador dpl
## 11                   dodge challenger se
## 12                    plymouth 'cuda 340
## 13                 chevrolet monte carlo
## 14               buick estate wagon (sw)
## 15                 toyota corona mark ii
## 16                       plymouth duster
## 17                            amc hornet
## 18                         ford maverick
## 19                          datsun pl510
## 20          volkswagen 1131 deluxe sedan
## 21                           peugeot 504
## 22                           audi 100 ls
## 23                              saab 99e
## 24                              bmw 2002
## 25                           amc gremlin
## 26                             ford f250
## 27                             chevy c20
## 28                            dodge d200
## 29                              hi 1200d
## 30                          datsun pl510
## 31                   chevrolet vega 2300
## 32                         toyota corona
## 34                           amc gremlin
## 35             plymouth satellite custom
## 36             chevrolet chevelle malibu
## 37                       ford torino 500
## 38                           amc matador
## 39                      chevrolet impala
## 40             pontiac catalina brougham
## 41                      ford galaxie 500
## 42                     plymouth fury iii
## 43                     dodge monaco (sw)
## 44              ford country squire (sw)
## 45                   pontiac safari (sw)
## 46            amc hornet sportabout (sw)
## 47                   chevrolet vega (sw)
## 48                      pontiac firebird
## 49                          ford mustang
## 50                    mercury capri 2000
## 51                             opel 1900
## 52                           peugeot 304
## 53                             fiat 124b
## 54                   toyota corolla 1200
## 55                           datsun 1200
## 56                  volkswagen model 111
## 57                      plymouth cricket
## 58                 toyota corona hardtop
## 59                    dodge colt hardtop
## 60                     volkswagen type 3
## 61                        chevrolet vega
## 62                   ford pinto runabout
## 63                      chevrolet impala
## 64                      pontiac catalina
## 65                     plymouth fury iii
## 66                      ford galaxie 500
## 67                    amc ambassador sst
## 68                       mercury marquis
## 69                  buick lesabre custom
## 70            oldsmobile delta 88 royale
## 71                chrysler newport royal
## 72                       mazda rx2 coupe
## 73                      amc matador (sw)
## 74      chevrolet chevelle concours (sw)
## 75                 ford gran torino (sw)
## 76        plymouth satellite custom (sw)
## 77                       volvo 145e (sw)
## 78                   volkswagen 411 (sw)
## 79                      peugeot 504 (sw)
## 80                       renault 12 (sw)
## 81                       ford pinto (sw)
## 82                       datsun 510 (sw)
## 83           toyouta corona mark ii (sw)
## 84                       dodge colt (sw)
## 85              toyota corolla 1600 (sw)
## 86                     buick century 350
## 87                           amc matador
## 88                      chevrolet malibu
## 89                      ford gran torino
## 90                  dodge coronet custom
## 91              mercury marquis brougham
## 92             chevrolet caprice classic
## 93                              ford ltd
## 94              plymouth fury gran sedan
## 95          chrysler new yorker brougham
## 96              buick electra 225 custom
## 97               amc ambassador brougham
## 98                      plymouth valiant
## 99                 chevrolet nova custom
## 100                           amc hornet
## 101                        ford maverick
## 102                      plymouth duster
## 103              volkswagen super beetle
## 104                     chevrolet impala
## 105                         ford country
## 106               plymouth custom suburb
## 107             oldsmobile vista cruiser
## 108                          amc gremlin
## 109                        toyota carina
## 110                       chevrolet vega
## 111                           datsun 610
## 112                            maxda rx3
## 113                           ford pinto
## 114                     mercury capri v6
## 115                 fiat 124 sport coupe
## 116              chevrolet monte carlo s
## 117                   pontiac grand prix
## 118                             fiat 128
## 119                           opel manta
## 120                           audi 100ls
## 121                          volvo 144ea
## 122                    dodge dart custom
## 123                            saab 99le
## 124                       toyota mark ii
## 125                     oldsmobile omega
## 126                      plymouth duster
## 128                           amc hornet
## 129                       chevrolet nova
## 130                          datsun b210
## 131                           ford pinto
## 132                  toyota corolla 1200
## 133                       chevrolet vega
## 134    chevrolet chevelle malibu classic
## 135                          amc matador
## 136           plymouth satellite sebring
## 137                     ford gran torino
## 138             buick century luxus (sw)
## 139            dodge coronet custom (sw)
## 140                ford gran torino (sw)
## 141                     amc matador (sw)
## 142                             audi fox
## 143                    volkswagen dasher
## 144                           opel manta
## 145                        toyota corona
## 146                           datsun 710
## 147                           dodge colt
## 148                             fiat 128
## 149                          fiat 124 tc
## 150                          honda civic
## 151                               subaru
## 152                            fiat x1.9
## 153              plymouth valiant custom
## 154                       chevrolet nova
## 155                      mercury monarch
## 156                        ford maverick
## 157                     pontiac catalina
## 158                    chevrolet bel air
## 159                  plymouth grand fury
## 160                             ford ltd
## 161                        buick century
## 162            chevroelt chevelle malibu
## 163                          amc matador
## 164                        plymouth fury
## 165                        buick skyhawk
## 166                  chevrolet monza 2+2
## 167                      ford mustang ii
## 168                       toyota corolla
## 169                           ford pinto
## 170                          amc gremlin
## 171                        pontiac astro
## 172                        toyota corona
## 173                    volkswagen dasher
## 174                           datsun 710
## 175                           ford pinto
## 176                    volkswagen rabbit
## 177                            amc pacer
## 178                           audi 100ls
## 179                          peugeot 504
## 180                          volvo 244dl
## 181                            saab 99le
## 182                     honda civic cvcc
## 183                             fiat 131
## 184                            opel 1900
## 185                             capri ii
## 186                           dodge colt
## 187                         renault 12tl
## 188    chevrolet chevelle malibu classic
## 189               dodge coronet brougham
## 190                          amc matador
## 191                     ford gran torino
## 192                     plymouth valiant
## 193                       chevrolet nova
## 194                        ford maverick
## 195                           amc hornet
## 196                   chevrolet chevette
## 197                      chevrolet woody
## 198                            vw rabbit
## 199                          honda civic
## 200                       dodge aspen se
## 201                    ford granada ghia
## 202                   pontiac ventura sj
## 203                        amc pacer d/l
## 204                    volkswagen rabbit
## 205                         datsun b-210
## 206                       toyota corolla
## 207                           ford pinto
## 208                            volvo 245
## 209           plymouth volare premier v8
## 210                          peugeot 504
## 211                       toyota mark ii
## 212                   mercedes-benz 280s
## 213                     cadillac seville
## 214                            chevy c10
## 215                            ford f108
## 216                           dodge d100
## 217                    honda accord cvcc
## 218              buick opel isuzu deluxe
## 219                        renault 5 gtl
## 220                    plymouth arrow gs
## 221                datsun f-10 hatchback
## 222            chevrolet caprice classic
## 223           oldsmobile cutlass supreme
## 224                dodge monaco brougham
## 225              mercury cougar brougham
## 226                   chevrolet concours
## 227                        buick skylark
## 228               plymouth volare custom
## 229                         ford granada
## 230                pontiac grand prix lj
## 231         chevrolet monte carlo landau
## 232                     chrysler cordoba
## 233                     ford thunderbird
## 234             volkswagen rabbit custom
## 235                pontiac sunbird coupe
## 236              toyota corolla liftback
## 237                  ford mustang ii 2+2
## 238                   chevrolet chevette
## 239                       dodge colt m/m
## 240                            subaru dl
## 241                    volkswagen dasher
## 242                           datsun 810
## 243                             bmw 320i
## 244                           mazda rx-4
## 245      volkswagen rabbit custom diesel
## 246                          ford fiesta
## 247                     mazda glc deluxe
## 248                       datsun b210 gx
## 249                     honda civic cvcc
## 250    oldsmobile cutlass salon brougham
## 251                       dodge diplomat
## 252                 mercury monarch ghia
## 253                   pontiac phoenix lj
## 254                     chevrolet malibu
## 255                 ford fairmont (auto)
## 256                  ford fairmont (man)
## 257                      plymouth volare
## 258                          amc concord
## 259                buick century special
## 260                       mercury zephyr
## 261                          dodge aspen
## 262                      amc concord d/l
## 263         chevrolet monte carlo landau
## 264      buick regal sport coupe (turbo)
## 265                          ford futura
## 266                      dodge magnum xe
## 267                   chevrolet chevette
## 268                        toyota corona
## 269                           datsun 510
## 270                           dodge omni
## 271            toyota celica gt liftback
## 272                     plymouth sapporo
## 273               oldsmobile starfire sx
## 274                        datsun 200-sx
## 275                            audi 5000
## 276                          volvo 264gl
## 277                           saab 99gle
## 278                        peugeot 604sl
## 279                  volkswagen scirocco
## 280                      honda accord lx
## 281                    pontiac lemans v6
## 282                     mercury zephyr 6
## 283                      ford fairmont 4
## 284                     amc concord dl 6
## 285                        dodge aspen 6
## 286            chevrolet caprice classic
## 287                      ford ltd landau
## 288                mercury grand marquis
## 289                      dodge st. regis
## 290              buick estate wagon (sw)
## 291             ford country squire (sw)
## 292        chevrolet malibu classic (sw)
## 293 chrysler lebaron town @ country (sw)
## 294                     vw rabbit custom
## 295                     maxda glc deluxe
## 296          dodge colt hatchback custom
## 297                        amc spirit dl
## 298                   mercedes benz 300d
## 299                    cadillac eldorado
## 300                          peugeot 504
## 301    oldsmobile cutlass salon brougham
## 302                     plymouth horizon
## 303                 plymouth horizon tc3
## 304                           datsun 210
## 305                   fiat strada custom
## 306                buick skylark limited
## 307                   chevrolet citation
## 308            oldsmobile omega brougham
## 309                      pontiac phoenix
## 310                            vw rabbit
## 311                toyota corolla tercel
## 312                   chevrolet chevette
## 313                           datsun 310
## 314                   chevrolet citation
## 315                        ford fairmont
## 316                          amc concord
## 317                          dodge aspen
## 318                            audi 4000
## 319               toyota corona liftback
## 320                            mazda 626
## 321                 datsun 510 hatchback
## 322                       toyota corolla
## 323                            mazda glc
## 324                           dodge colt
## 325                           datsun 210
## 326                 vw rabbit c (diesel)
## 327                   vw dasher (diesel)
## 328                  audi 5000s (diesel)
## 329                   mercedes-benz 240d
## 330                  honda civic 1500 gl
## 332                            subaru dl
## 333                     vokswagen rabbit
## 334                        datsun 280-zx
## 335                        mazda rx-7 gs
## 336                    triumph tr7 coupe
## 338                         honda accord
## 339                     plymouth reliant
## 340                        buick skylark
## 341               dodge aries wagon (sw)
## 342                   chevrolet citation
## 343                     plymouth reliant
## 344                       toyota starlet
## 345                       plymouth champ
## 346                     honda civic 1300
## 347                               subaru
## 348                       datsun 210 mpg
## 349                        toyota tercel
## 350                          mazda glc 4
## 351                   plymouth horizon 4
## 352                       ford escort 4w
## 353                       ford escort 2h
## 354                     volkswagen jetta
## 356                        honda prelude
## 357                       toyota corolla
## 358                         datsun 200sx
## 359                            mazda 626
## 360            peugeot 505s turbo diesel
## 361                         volvo diesel
## 362                      toyota cressida
## 363                    datsun 810 maxima
## 364                        buick century
## 365                oldsmobile cutlass ls
## 366                      ford granada gl
## 367               chrysler lebaron salon
## 368                   chevrolet cavalier
## 369             chevrolet cavalier wagon
## 370            chevrolet cavalier 2-door
## 371           pontiac j2000 se hatchback
## 372                       dodge aries se
## 373                      pontiac phoenix
## 374                 ford fairmont futura
## 375                  volkswagen rabbit l
## 376                   mazda glc custom l
## 377                     mazda glc custom
## 378               plymouth horizon miser
## 379                       mercury lynx l
## 380                     nissan stanza xe
## 381                         honda accord
## 382                       toyota corolla
## 383                          honda civic
## 384                   honda civic (auto)
## 385                        datsun 310 gx
## 386                buick century limited
## 387    oldsmobile cutlass ciera (diesel)
## 388           chrysler lebaron medallion
## 389                       ford granada l
## 390                     toyota celica gt
## 391                    dodge charger 2.2
## 392                     chevrolet camaro
## 393                      ford mustang gl
## 394                            vw pickup
## 395                        dodge rampage
## 396                          ford ranger
## 397                           chevy s-10
dim(na.omit(Auto))
## [1] 392   9

1.5 Additional summaries

Scatterplot of quantitative variables

plot(cylinders , mpg)
## Error in plot(cylinders, mpg): object 'cylinders' not found

To refer to a variable, we must type the data set and the variable name joined with a $ symbol.

DO NOT USE attach()

plot(Auto$cylinders, Auto$mpg)

plot(Auto$cylinders)

# but this is actually a factor...

Auto$cylinders <- as.factor(Auto$cylinders)
plot(Auto$cylinders, Auto$mpg)

plot(Auto$cylinders)

# customizing the aspect
plot(Auto$cylinders, Auto$mpg, col="red", varwidth=T, xlab="cylinders", ylab = "MPG")

plot(Auto$cylinders, Auto$mpg, col="red", horizontal=T, xlab="cylinders", ylab = "MPG")

Histogram

hist(Auto$mpg)

hist(Auto$mpg, col = 2)

hist(Auto$mpg, breaks=15)

Scatterplot matrix

pairs(Auto)

# for just a subset
pairs(~mpg + displacement + horsepower + weight, Auto)

identify(): a useful interactive method for identifying the value for a particular variable for points on a plot.

plot(Auto$horsepower, Auto$mpg)
identify(Auto$horsepower,Auto$mpg,Auto$name)

## integer(0)
# click, click, click, and then ESC

One of your best friends: summary(), to produce a numerical summary of each variable in a particular data set

summary(Auto)
##       mpg        cylinders  displacement     horsepower        weight    
##  Min.   : 9.00   3:  4     Min.   : 68.0   Min.   : 46.0   Min.   :1613  
##  1st Qu.:17.00   4:199     1st Qu.:105.0   1st Qu.: 75.0   1st Qu.:2225  
##  Median :22.75   5:  3     Median :151.0   Median : 93.5   Median :2804  
##  Mean   :23.45   6: 83     Mean   :194.4   Mean   :104.5   Mean   :2978  
##  3rd Qu.:29.00   8:103     3rd Qu.:275.8   3rd Qu.:126.0   3rd Qu.:3615  
##  Max.   :46.60             Max.   :455.0   Max.   :230.0   Max.   :5140  
##                                                                          
##   acceleration        year           origin                      name    
##  Min.   : 8.00   Min.   :70.00   Min.   :1.000   amc matador       :  5  
##  1st Qu.:13.78   1st Qu.:73.00   1st Qu.:1.000   ford pinto        :  5  
##  Median :15.50   Median :76.00   Median :1.000   toyota corolla    :  5  
##  Mean   :15.54   Mean   :75.98   Mean   :1.577   amc gremlin       :  4  
##  3rd Qu.:17.02   3rd Qu.:79.00   3rd Qu.:2.000   amc hornet        :  4  
##  Max.   :24.80   Max.   :82.00   Max.   :3.000   chevrolet chevette:  4  
##                                                  (Other)           :365
summary(Auto$mpg)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    9.00   17.00   22.75   23.45   29.00   46.60
summary(Auto$cylinders)
##   3   4   5   6   8 
##   4 199   3  83 103

Done for today

q()
quit()

but first, you can savehistory("history_filename.R") - still, I would recommend to always use a script anyway!

2 Chapter 2 Exercises

2.4 Exercises Conceptual 1. For each of parts (a) through (d), indicate whether we would generally expect the performance of a flexible statistical learning method to be better or worse than an inflexible method. Justify your answer. (a) The sample size n is extremely large, and the number of predic- tors p is small. (b) The number of predictors p is extremely large, and the number of observations n is small. (c) The relationship between the predictors and response is highly non-linear. (d) The variance of the error terms, i.e. σ2 = Var(ε), is extremely high. 2. Explain whether each scenario is a classification or regression prob- lem, and indicate whether we are most interested in inference or pre- diction. Finally, provide n and p. (a) We collect a set of data on the top 500 firms in the US. For each firm we record profit, number of employees, industry and the CEO salary. We are interested in understanding which factors affect CEO salary. (b) We are considering launching a new product and wish to know whether it will be a success or a failure. We collect data on 20 similar products that were previously launched. For each prod- uct we have recorded whether it was a success or failure, price charged for the product, marketing budget, competition price, and ten other variables. (c) We are interested in predicting the % change in the USD/Euro exchange rate in relation to the weekly changes in the world stock markets. Hence we collect weekly data for all of 2012. For each week we record the % change in the USD/Euro, the % change in the US market, the % change in the British market, and the % change in the German market. 3. We now revisit the bias-variance decomposition. (a) Provide a sketch of typical (squared) bias, variance, training er- ror, test error, and Bayes (or irreducible) error curves, on a sin- gle plot, as we go from less flexible statistical learning methods towards more flexible approaches. The x-axis should represent 4. You ing. will now think of some real-life applications for statistical learn- the amount of flexibility in the method, and the y-axis should represent the values for each curve. There should be five curves. Make sure to label each one. (b) Explain why each of the five curves has the shape displayed in part (a). (a) Describe three real-life applications in which classification might be useful. Describe the response, as well as the predictors. Is the goal of each application inference or prediction? Explain your answer. (b) Describe three real-life applications in which regression might be useful. Describe the response, as well as the predictors. Is the goal of each application inference or prediction? Explain your answer. (c) Describe three real-life applications in which cluster analysis might be useful. 5. What are the advantages and disadvantages of a very flexible (versus a less flexible) approach for regression or classification? Under what circumstances might a more flexible approach be preferred to a less flexible approach? When might a less flexible approach be preferred? 6. Describe the differences between a parametric and a non-parametric statistical learning approach. What are the advantages of a para- metric approach to regression or classification (as opposed to a non- parametric approach)? What are its disadvantages? 7. The table below provides a training data set containing six observa- tions, three predictors, and one qualitative response variable. Obs. X1 X2 X3 Y 1 030Red 2 200Red 3 013Red 4 012Green 5 −1 0 1 Green 6 111Red Suppose we wish to use this data set to make a prediction for Y when X1 = X2 = X3 = 0 using K-nearest neighbors. (a) Compute the Euclidean distance between each observation and thetestpoint,X1 =X2 =X3 =0.

2.4 Exercises 53

54 2. Statistical Learning (b) What is our prediction with K = 1? Why? (c) What is our prediction with K = 3? Why? (d) If the Bayes decision boundary in this problem is highly non- linear, then would we expect the best value for K to be large or small? Why? Applied 8. This exercise relates to the College data set, which can be found in the file College.csv. It contains a number of variables for 777 different universities and colleges in the US. The variables are • Private : Public/private indicator • Apps : Number of applications received • Accept : Number of applicants accepted • Enroll : Number of new students enrolled • Top10perc : New students from top 10 % of high school class • Top25perc : New students from top 25 % of high school class • F.Undergrad : Number of full-time undergraduates • P.Undergrad : Number of part-time undergraduates • Outstate : Out-of-state tuition • Room.Board : Room and board costs • Books : Estimated book costs • Personal : Estimated personal spending • PhD : Percent of faculty with Ph.D.’s • Terminal : Percent of faculty with terminal degree • S.F.Ratio : Student/faculty ratio • perc.alumni : Percent of alumni who donate • Expend : Instructional expenditure per student • Grad.Rate : Graduation rate Before reading the data into R, it can be viewed in Excel or a text editor. (a) Use the read.csv() function to read the data into R. Call the loaded data college. Make sure that you have the directory set to the correct location for the data. (b) Look at the data using the fix() function. You should notice that the first column is just the name of each university. We don’t really want R to treat this as data. However, it may be handy to have these names for later. Try the following commands: 2.4 Exercises 55 (c) > rownames(college)=college[,1] > fix(college) You should see that there is now a row.names column with the name of each university recorded. This means that R has given each row a name corresponding to the appropriate university. R will not try to perform calculations on the row names. However, we still need to eliminate the first column in the data where the names are stored. Try > college=college[,-1] > fix(college) Now you should see that the first data column is Private. Note that another column labeled row.names now appears before the Private column. However, this is not a data column but rather the name that R is giving to each row. i. Use the summary() function to produce a numerical summary of the variables in the data set. ii. Use the pairs() function to produce a scatterplot matrix of the first ten columns or variables of the data. Recall that you can reference the first ten columns of a matrix A using A[,1:10]. iii. Use the plot() function to produce side-by-side boxplots of Outstate versus Private. iv. Create a new qualitative variable, called Elite, by binning the Top10perc variable. We are going to divide universities into two groups based on whether or not the proportion of students coming from the top 10% of their high school classes exceeds 50 %. > Elite=rep(“No”,nrow(college)) > Elite[college$Top10perc >50]=“Yes” > Elite=as.factor(Elite) > college=data.frame(college ,Elite) Use the summary() function to see how many elite univer- sities there are. Now use the plot() function to produce side-by-side boxplots of Outstate versus Elite. v. Use the hist() function to produce some histograms with differing numbers of bins for a few of the quantitative vari- ables. You may find the command par(mfrow=c(2,2)) useful: it will divide the print window into four regions so that four plots can be made simultaneously. Modifying the arguments to this function will divide the screen in other ways. vi. Continue exploring the data, and provide a brief summary of what you discover.

56 2. Statistical Learning 9. This exercise involves the Auto data set studied in the lab. Make sure that the missing values have been removed from the data. (a) Which of the predictors are quantitative, and which are quali- tative? (b) What is the range of each quantitative predictor? You can an- swer this using the range() function. (c) What is the mean and standard deviation of each quantitative predictor? (d) Now remove the 10th through 85th observations. What is the range, mean, and standard deviation of each predictor in the subset of the data that remains? (e) Using the full data set, investigate the predictors graphically, using scatterplots or other tools of your choice. Create some plots highlighting the relationships among the predictors. Comment on your findings. (f) Suppose that we wish to predict gas mileage (mpg) on the basis of the other variables. Do your plots suggest that any of the other variables might be useful in predicting mpg? Justify your answer. 10. This exercise involves the Boston housing data set. (a) To begin, load in the Boston data set. The Boston data set is part of the MASS library in R. > library(MASS) Now the data set is contained in the object Boston. > Boston Read about the data set: > ?Boston How many rows are in this data set? How many columns? What do the rows and columns represent? (b) Make some pairwise scatterplots of the predictors (columns) in this data set. Describe your findings. (c) Are any of the predictors associated with per capita crime rate? If so, explain the relationship. (d) Do any of the suburbs of Boston appear to have particularly high crime rates? Tax rates? Pupil-teacher ratios? Comment on the range of each predictor. (e) How many of the suburbs in this data set bound the Charles river? range()

  1. What is the median pupil-teacher ratio among the towns in this data set?
  2. Which suburb of Boston has lowest median value of owner- occupied homes? What are the values of the other predictors for that suburb, and how do those values compare to the overall ranges for those predictors? Comment on your findings.
  3. In this data set, how many of the suburbs average more than seven rooms per dwelling? More than eight rooms per dwelling? Comment on the suburbs that average more than eight rooms per dwelling.
---
title: >
  ISL - Chapter 2 Labs
author: Federico Marini
output: 
  html_document:
  # BiocStyle::html_document:
    toc: true
    toc_float: true
    number_sections: true
    theme: cosmo
    code_folding: show
    code_download: true
editor_options: 
  chunk_output_type: console

---

# Chapter 2 Lab: Introduction to R

This one is indeed a soft intro!

No worry to make things wrong: TRY!

Got R?

- R can be downloaded from http://cran.r-project.org/

Start...

- an R script (tired!)
- an R Markdown document (wired!)

## Basic commands

Functions are noted as `funcname(input1, input2)` - `input`s are called _arguments_

Creating a vector by `c`oncatenating

```{r}
c(1, 3, 2, 5)
x <- c(1, 3, 2, 5) # use <- for assignment, leave = for parameter values
x

x = c(1,6,2)
y = c(1,4,3)
```

Navigating history:

- up arrow
- ctrl + up (RStudio) while typing part of the command

Help:

- use `?`
- `help(funcname)`

Length (of a vector)

```{r}
length(x)
length(y)
```

Adding things together

```{r}
1 + 4
x + y # if same length
x + 1
x + c(1,2)
```


Listing objects, removing them

```{r}
ls()
rm(x, y)
ls()
```

Create a matrix of numbers

```{r}
?matrix
x <- matrix(data=c(1,2,3,4), nrow=2, ncol=2)
x
x <- matrix(data=c(1,2,3,4), 2, 2)
x
# Recommended: specify arguments!
matrix(c(1,2,3,4),2,2,byrow=TRUE)
```

Squaring, squared root

```{r}
x
sqrt(x)
sqrt(x)[,1]
x^2
```

Random normal variables, with `rnorm`

```{r}
# bonus - when dealing with random quantities!
set.seed(42)

x <- rnorm(50)
# default: mean of 0 and standard deviation of 1
y <- x + rnorm(50,mean=50,sd=.1) 
```

Computing the correlation between two sets of numbers

```{r}
cor(x,y)
```

Mean & Standard deviation

```{r}
mean(x)
sd(x)
mean(y)
sd(y)
var(x)
var(y)

set.seed(3)
y <- rnorm(100)
mean(y)
var(y)
sqrt(var(y))
sd(y)
```


## Graphics

Meet the `plot()` function!

`plot(x,y)`

```{r}
?plot
```


The plot() function is the primary way to plot data in R. For instance, plot(x,y) produces a scatterplot of the numbers in x versus the numbers in y. There are many additional options that can be passed in to the plot() function. For example, passing in the argument xlab will result in a label on the x-axis. To find out more information about the plot() function, type ?plot.

```{r}
set.seed(42)
x <- rnorm(100)
y <- rnorm(100)
plot(x,y)
plot(x,y,
     xlab="this is the x-axis",
     ylab="this is the y-axis",
     main="Plot of X vs Y")
# plot()
```
      
Saving the output:

```
open device
plot...
close device
```

```{r}
pdf("Figure.pdf")
plot(x,y,col="green")
dev.off()
```

Devices: `pdf()`, `jpeg()`, ...

Creating `seq`uences of numbers

```{r}
?seq
seq(0,1)
seq(0,1,length=10)
pi
seq(-pi,pi,length=50)
```

Some more complex plots:

- `contour()` to represent 3d data

```{r}
?contour
?outer

# assignment and printing trick ;)
(x <- seq(-pi,pi,length=50))
y <- x
f <- outer(x,y,function (x,y)cos(y)/(1+x^2))
f
contour(x, y, f)
contour(x,y,f,nlevels=45,add=T)
fa <- (f-t(f))/2
contour(x,y,fa,nlevels=15)
```

- `image()` to produce a color-coded plot whose colors depend on the z value (a.k.a. heatmap)

```{r}
image(x,y,fa)
```


- `persp()` to produce a three-dimensional plot
known as a heatmap, and is sometimes used to plot temperature in weather forecasts. Alternatively, persp() can be used to . The arguments theta and phi control the angles at which the plot is persp() viewed.

```{r}
persp(x,y,fa)
persp(x,y,fa,theta=30)
persp(x,y,fa,theta=30,phi=20)
persp(x,y,fa,theta=30,phi=70)
persp(x,y,fa,theta=30,phi=40)
```

## Indexing data

Examining a subset of a dataset `A`

```{r}
A <- matrix(1:16,4,4)
A
A[2,3]
A[c(1,3),c(2,4)]
A[1:3,2:4]
A[1,]
A[1:2,]
A[,1:2]
A[-c(1,3),]
```

`dim`ensions

```{r}
dim(A)
```


## Loading data

```{r}
library(ISLR)
Auto
write.table(Auto, file = "Auto.txt")
read.table(file = "Auto.txt")

?read.csv

# fix(Auto)
View(Auto)
knitr::kable(Auto)
class(Auto)
dim(Auto)
names(Auto)
str(Auto)
na.omit(Auto)
dim(na.omit(Auto))
```


## Additional summaries

Scatterplot of quantitative variables

```{r, error=TRUE}
plot(cylinders , mpg)
```


To refer to a variable, we must type the data set and the variable name joined with a `$` symbol.

DO NOT USE `attach()`

```{r}
plot(Auto$cylinders, Auto$mpg)
plot(Auto$cylinders)

# but this is actually a factor...

Auto$cylinders <- as.factor(Auto$cylinders)
plot(Auto$cylinders, Auto$mpg)
plot(Auto$cylinders)

# customizing the aspect
plot(Auto$cylinders, Auto$mpg, col="red", varwidth=T, xlab="cylinders", ylab = "MPG")
plot(Auto$cylinders, Auto$mpg, col="red", horizontal=T, xlab="cylinders", ylab = "MPG")

```

Histogram

```{r}
hist(Auto$mpg)
hist(Auto$mpg, col = 2)
hist(Auto$mpg, breaks=15)
```

Scatterplot matrix

```{r, fig.width=10, fig.height=10}
pairs(Auto)

# for just a subset
pairs(~mpg + displacement + horsepower + weight, Auto)
```


`identify()`: a useful interactive method for identifying the value for a particular variable for points on a plot. 

```{r}
plot(Auto$horsepower, Auto$mpg)
identify(Auto$horsepower,Auto$mpg,Auto$name)
# click, click, click, and then ESC
```

One of your best friends: `summary()`, to produce a numerical summary of each variable in a particular data set

```{r}
summary(Auto)
summary(Auto$mpg)
summary(Auto$cylinders)
```

Done for today

```{r eval=FALSE}
q()
quit()
```

but first, you can `savehistory("history_filename.R")` - still, I would recommend to always use a script anyway!


# Chapter 2 Exercises 

2.4 Exercises
Conceptual
1. For each of parts (a) through (d), indicate whether we would generally expect the performance of a flexible statistical learning method to be better or worse than an inflexible method. Justify your answer.
(a) The sample size n is extremely large, and the number of predic- tors p is small.
(b) The number of predictors p is extremely large, and the number of observations n is small.
(c) The relationship between the predictors and response is highly non-linear.
(d) The variance of the error terms, i.e. σ2 = Var(ε), is extremely high.
2. Explain whether each scenario is a classification or regression prob- lem, and indicate whether we are most interested in inference or pre- diction. Finally, provide n and p.
(a) We collect a set of data on the top 500 firms in the US. For each firm we record profit, number of employees, industry and the CEO salary. We are interested in understanding which factors affect CEO salary.
(b) We are considering launching a new product and wish to know whether it will be a success or a failure. We collect data on 20 similar products that were previously launched. For each prod- uct we have recorded whether it was a success or failure, price charged for the product, marketing budget, competition price, and ten other variables.
(c) We are interested in predicting the % change in the USD/Euro exchange rate in relation to the weekly changes in the world stock markets. Hence we collect weekly data for all of 2012. For each week we record the % change in the USD/Euro, the % change in the US market, the % change in the British market, and the % change in the German market.
3. We now revisit the bias-variance decomposition.
(a) Provide a sketch of typical (squared) bias, variance, training er- ror, test error, and Bayes (or irreducible) error curves, on a sin- gle plot, as we go from less flexible statistical learning methods towards more flexible approaches. The x-axis should represent
4. You ing.
will now think of some real-life applications for statistical learn-
the amount of flexibility in the method, and the y-axis should represent the values for each curve. There should be five curves. Make sure to label each one.
(b) Explain why each of the five curves has the shape displayed in part (a).
(a) Describe three real-life applications in which classification might be useful. Describe the response, as well as the predictors. Is the goal of each application inference or prediction? Explain your answer.
(b) Describe three real-life applications in which regression might be useful. Describe the response, as well as the predictors. Is the goal of each application inference or prediction? Explain your answer.
(c) Describe three real-life applications in which cluster analysis might be useful.
5. What are the advantages and disadvantages of a very flexible (versus a less flexible) approach for regression or classification? Under what circumstances might a more flexible approach be preferred to a less flexible approach? When might a less flexible approach be preferred?
6. Describe the differences between a parametric and a non-parametric statistical learning approach. What are the advantages of a para- metric approach to regression or classification (as opposed to a non- parametric approach)? What are its disadvantages?
7. The table below provides a training data set containing six observa- tions, three predictors, and one qualitative response variable.
Obs. X1 X2 X3 Y
1 030Red
2 200Red
3 013Red
4 012Green 5 −1 0 1 Green 6 111Red
Suppose we wish to use this data set to make a prediction for Y when X1 = X2 = X3 = 0 using K-nearest neighbors.
(a) Compute the Euclidean distance between each observation and thetestpoint,X1 =X2 =X3 =0.






2.4 Exercises 53
          
54
2. Statistical Learning
(b) What is our prediction with K = 1? Why?
(c) What is our prediction with K = 3? Why?
(d) If the Bayes decision boundary in this problem is highly non- linear, then would we expect the best value for K to be large or small? Why?
Applied
8. This exercise relates to the College data set, which can be found in the file College.csv. It contains a number of variables for 777 different universities and colleges in the US. The variables are
• Private : Public/private indicator
• Apps : Number of applications received
• Accept : Number of applicants accepted
• Enroll : Number of new students enrolled
• Top10perc : New students from top 10 % of high school class • Top25perc : New students from top 25 % of high school class • F.Undergrad : Number of full-time undergraduates
• P.Undergrad : Number of part-time undergraduates
• Outstate : Out-of-state tuition
• Room.Board : Room and board costs
• Books : Estimated book costs
• Personal : Estimated personal spending
• PhD : Percent of faculty with Ph.D.’s
• Terminal : Percent of faculty with terminal degree
• S.F.Ratio : Student/faculty ratio
• perc.alumni : Percent of alumni who donate
• Expend : Instructional expenditure per student
• Grad.Rate : Graduation rate
Before reading the data into R, it can be viewed in Excel or a text editor.
(a) Use the read.csv() function to read the data into R. Call the loaded data college. Make sure that you have the directory set to the correct location for the data.
(b) Look at the data using the fix() function. You should notice that the first column is just the name of each university. We don’t really want R to treat this as data. However, it may be handy to have these names for later. Try the following commands:
2.4 Exercises 55
    (c)
> rownames(college)=college[,1] > fix(college)
You should see that there is now a row.names column with the name of each university recorded. This means that R has given each row a name corresponding to the appropriate university. R will not try to perform calculations on the row names. However, we still need to eliminate the first column in the data where the names are stored. Try
> college=college[,-1] > fix(college)
Now you should see that the first data column is Private. Note that another column labeled row.names now appears before the Private column. However, this is not a data column but rather the name that R is giving to each row.
i. Use the summary() function to produce a numerical summary of the variables in the data set.
ii. Use the pairs() function to produce a scatterplot matrix of the first ten columns or variables of the data. Recall that you can reference the first ten columns of a matrix A using A[,1:10].
iii. Use the plot() function to produce side-by-side boxplots of Outstate versus Private.
iv. Create a new qualitative variable, called Elite, by binning the Top10perc variable. We are going to divide universities into two groups based on whether or not the proportion of students coming from the top 10% of their high school classes exceeds 50 %.
> Elite=rep("No",nrow(college))
> Elite[college$Top10perc >50]="Yes"
> Elite=as.factor(Elite)
> college=data.frame(college ,Elite)
Use the summary() function to see how many elite univer- sities there are. Now use the plot() function to produce side-by-side boxplots of Outstate versus Elite.
v. Use the hist() function to produce some histograms with differing numbers of bins for a few of the quantitative vari- ables. You may find the command par(mfrow=c(2,2)) useful: it will divide the print window into four regions so that four plots can be made simultaneously. Modifying the arguments to this function will divide the screen in other ways.
vi. Continue exploring the data, and provide a brief summary of what you discover.
           
56
2. Statistical Learning
9. This exercise involves the Auto data set studied in the lab. Make sure that the missing values have been removed from the data.
(a) Which of the predictors are quantitative, and which are quali- tative?
(b) What is the range of each quantitative predictor? You can an- swer this using the range() function.
(c) What is the mean and standard deviation of each quantitative predictor?
(d) Now remove the 10th through 85th observations. What is the range, mean, and standard deviation of each predictor in the subset of the data that remains?
(e) Using the full data set, investigate the predictors graphically, using scatterplots or other tools of your choice. Create some plots highlighting the relationships among the predictors. Comment on your findings.
(f) Suppose that we wish to predict gas mileage (mpg) on the basis of the other variables. Do your plots suggest that any of the other variables might be useful in predicting mpg? Justify your answer.
10. This exercise involves the Boston housing data set.
(a) To begin, load in the Boston data set. The Boston data set is
part of the MASS library in R. > library(MASS)
Now the data set is contained in the object Boston. > Boston
Read about the data set:
> ?Boston
How many rows are in this data set? How many columns? What do the rows and columns represent?
(b) Make some pairwise scatterplots of the predictors (columns) in this data set. Describe your findings.
(c) Are any of the predictors associated with per capita crime rate? If so, explain the relationship.
(d) Do any of the suburbs of Boston appear to have particularly high crime rates? Tax rates? Pupil-teacher ratios? Comment on the range of each predictor.
(e) How many of the suburbs in this data set bound the Charles river?
range()
   
(f) What is the median pupil-teacher ratio among the towns in this data set?
(g) Which suburb of Boston has lowest median value of owner- occupied homes? What are the values of the other predictors for that suburb, and how do those values compare to the overall ranges for those predictors? Comment on your findings.
(h) In this data set, how many of the suburbs average more than seven rooms per dwelling? More than eight rooms per dwelling? Comment on the suburbs that average more than eight rooms per dwelling.

